The Reds dominated possession for long spells, but it was West Brom who came closest to breaking the deadlock in the first half when Hal Robson-Kanu struck the crossbar.
Find out how all of the action unfolded courtesy of Sports Mole's minute-by-minute coverage below.
Results yesterday saw both clubs suffer notable slips down the table, with Liverpool dropping out of the top four and West Brom sinking into the relegation zone, but they have a chance to respond today in this midweek Premier League fixture.
We will have a closer look at both clubs a little later, but first let's check out the team news...
Well, there is really only one place to start and that is with Liverpool's attackers as the front four are all present for the hosts tonight. Klopp received some flak for the controversial decision to rest Coutinho and Firmino for the match against Everton at the weekend, and there were reports that he would continue his rotation this afternoon with Salah perhaps missing out, but the Brazilian duo, Salah and Mane are all involved from the off here.
Bad news for the Baggies!
The winger's stunning strike against Everton in Sunday's derby was his 19th of the season from just 24 games in all competitions, already equalling his Roma tally for 2016-17 which took him 41 matches to reach. It is more goals than any Liverpool player has managed in a season since Luis Suarez left the club, and also more than any other Premier League player this season.
West Brom cannot afford to focus solely on the Egyptian, though, with Firmino and Mane both capable of hurting the visitors as well. The last time all four played together Liverpool beat Spartak Moscow 7-0, so this will be a huge test for West Brom tonight.
The German makes a further six changes tonight too, including a surprise start for Loris Karius in goal ahead of Mignolet. Alexander-Arnold replaces Gomez at right-back, while Georginio Wijnaldum and Emre Can also return to the side in place of Oxlade-Chamberlain and captain Milner.
Jay Rodriguez does drop out of the side to be replaced by the more defensively-minded James McClean, but Salomon Rondon and Hal Robson-Kanu retain their places in a lineup slightly more attacking than we were expecting to see from the visitors.
Aside from Rodriguez making way there is just one other change for West Brom tonight, with Krychowiak replacing youngster Sam Field in the side.
Livermore and Krychowiak do have the ability to make a difference going forward too, but in the absence of the injured Gareth Barry their main task this evening will be to keep the likes of Coutinho, Can and Wijnaldum quiet in the middle of the park.
Hegazi, Evans and Gibbs make up that back four, while Chris Brunt - who starts on the bench tonight - could become the first player to make 250 Premier League appearances for West Brom tonight.
The Reds utterly dominated Everton from the very first whistle at Anfield, enjoying 79% possession throughout the match and peppering the Everton goal with 23 shots. Only one of those went in, though, and their wastefulness was punished in the final 15 minutes when Wayne Rooney rescued a smash-and-grab point.
Even if Liverpool have been made to pay for missing some chances, though, it is impossible to argue with their goalscoring statistics this season, with 63 from their 25 competitive outings so far making for their highest tally at this stage of a campaign since 1986-87.
Only three of the 20 Premier League goals they have conceded this season have come here at Anfield, making up just 15%, although they have also scored fewer in front of their own fans (14 at home, 20 away).
The Reds have kept five clean sheets in those last seven home games, compared to only two clean sheets away from home all season, so there is no doubt that they are a lot more defensively sound in front of their own fans.
The Reds are one of only two teams yet to lose a home league game this term, but both Manchester club, Arsenal and Burnley have all picked up more points in front of their own fans so Liverpool still have some catching up to do in that regard.
Victory tonight would be enough for the Reds to restore their place in the top four, but a second consecutive slip-up in a match which they are expected to win could see them finish the night as low as seventh, with Arsenal and Tottenham Hotspur both also in action tonight.
Klopp's side are also unbeaten at home so far this season - indeed stretching all the way back to April - although six of those 14 matches have ended all square.
Such a result would be something of a bittersweet moment, though, as it would also see the Baggies set an unwanted club record of 16 consecutive matches without a win in all competitions. Their current tally of 15 equals a run they went on in 1995-96, but never before in their 139-year history have they had to wait 16 games for a victory.
West Brom are 14 league games without a win - unsurprisingly the longest ongoing run in the division - losing half of those to leave themselves with their lowest points haul at this stage of a season since 2008-09.
Crystal Palace's dramatic late comeback against Watford last night was enough to plunge West Brom into the relegation zone, now one point from safety. A surprise win for the Baggies could lift them as high as 15th, but defeat could see them slump to the bottom of the table depending on the West Ham and Swansea results.
The going gets much tougher now, with Liverpool and Manchester United to come in their next two before a trip to Stoke City and home matches against Everton and Arsenal take them through to the New Year.
Goalscoring has been a major problem for West Brom all season, with only Swansea scoring fewer in the top flight this term and seven of their ongoing 14-match winless streak seeing the Baggies fail to score.
The Baggies' August victory at Burnley is their only Premier League away win of 2017 so far, picking up just nine points from a possible 51 in that time. Their hopes of improving that run at Anfield look to be slim tonight.
It has often come late on in games too, with West Brom conceding seven times in the final 16 minutes of matches already this season, which has cost them 12 points. Had they not thrown all of those points away then West Brom would be sitting in eighth place right now.
Liverpool may have thrown two points away here on Sunday but I cannot see the same happening again tonight, particularly with their 'Fab Four' all playing. West Brom don't concede many, but they score even fewer and their dreadful away form cannot be ignored. I'm going for a comfortable home win!
SPORTS MOLE SAYS: Liverpool 2-0 West Brom
West Brom had won three in a row against Liverpool before that run, though, and over the slightly more extended recent history the record between these two sides is surprisingly even. Liverpool won all of their first nine Premier League games against West Brom, but they have won five, drawn four and lost four of the subsequent 13.
That represents a major improvement on the goal front at Anfield, having taken 22 games to score their previous eight goals at the famous stadium, failing to find the back of the net 14 times during that spell.
The corresponding fixture at Anfield saw Mane and Coutinho score in the first half, before Gareth McAuley pulled one back nine minutes from time to prevent Liverpool from going top of the table on goal difference.
LIVERPOOL STARTING XI: Karius; Alexander-Arnold, Klavan, Lovren, Robertson; Wijnaldum, Can, Coutinho; Salah, Firmino, Mane
WEST BROM STARTING XI: Foster; Nyom, Hegazi, Evans, Gibbs; Livermore, Yacob, Krychowiak; McClean, Rondon, Robson-Kanu
Liverpool have dominated possession, as expected, but they have found it difficult to break through this West Brom defence and the Baggies have actually come closest to scoring so far. It is very finely poised heading into the second half.
Firmino did have Coutinho in support and his compatriot would have been left with a simple finish into an empty net, although Firmino cannot really be blamed for going for goal himself.
The shot never really looked like going in, but it took a sharp dip at the end of its trajectory to clip the top of the woodwork on its way behind.
It will be interesting to see whether the Baggies take encouragement from that first half and go even more attacking in the second half, or whether they are happy to settle for a point.
The Reds thought they had broken the deadlock with eight minutes remaining when Solanke bundled the ball home from close range, but referee Paul Tierney belatedly disallowed it for a handball - a decision which is sure to cause plenty of debate. The ball did come off Solanke's arm last, but it was entirely unintentional from the striker.
Thank you very much for joining Sports Mole for tonight's Premier League clash as Liverpool are held by West Brom at Anfield, missing the chance to move back into the top four as a result. I will leave you with our match report, and be sure to stick around for reaction too.
From me, though, it is goodbye for now!