The ex-Sweden international, who now has 14 goals in his first 20 league games in English football, pounced to cancel out James Milner's first-half penalty.
Liverpool had been on course for a first win in four attempts this calendar year, and a rare triumph at the home of their North-West rivals, but Ibrahimovic once again proved to be the star for his side as the spoils were shared.
Not until a quarter of the way through the match did the first opportunity present itself to United, who almost took the lead through Ibrahimovic's harrying - the striker closing down a slack back-pass and seeing the ball ricochet onto the roof of the net.
Just a minute or so later came a glimpse of United at their finest, as Henrikh Mkhitaryan slotted the ball through for Paul Pogba to latch on to, but he scuffed his shot under pressure and the chance went begging.
Liverpool's high pressing had unsettled their opponents in the early stages of the game and, while they were struggling to create any clear-cut openings of their own, Jurgen Klopp would have been happy enough with the energy on show from his side.
Even better was to come for Klopp 27 minutes in, however, with Milner tucking away from the spot - making it 10 from his last 10 to be successfully converted in the league - after Pogba handled a cross into the box.
The Red Devils were well on top after falling behind, coming close to a near-instant response when Ibrahimovic belted the ball on goal from a free kick for Simon Mignolet to palm away, before Mkhitaryan was also denied by the Liverpool keeper when played clean through on goal.
With his side at risk of seeing their impressive unbeaten run come to an end, Jose Mourinho turned to skipper Wayne Rooney at half time as he went in search of Sir Bobby Charlton's club-record goals tally.
There was an open feel to the second half but it was still the hosts who were creating the better chances, the best of which fell the way of Mkhitaryan yet again.
The Armenian was played through down the right by Ibrahimovic, before opting to pick out Anthony Martial - the player who started the counter from deep - rather than taking it on himself, which proved to be the wrong choice as his teammate failed to connect.
For all of United's possession it perhaps should have been game over shortly after the hour, as Philippe Coutinho - a minute after being brought off the bench for his first Prem outing in over two months - picked out Roberto Firmino who in turn was thwarted by David de Gea.
Georginio Wijnaldum then nodded over when picked out inside the box in what was a gripping second half, though it was to be the Red Devils who asked all the questions as the game entered its final 10 minutes.
After holding off their rivals for the best part of an hour, Liverpool came unstuck as sub Marouane Fellaini glanced the ball onto the post, before Antonio Valencia helped it back in for Ibrahimovic to lift over the reach of Mignolet.
United, who had won nine in a row in all competitions prior to this match, may have seen the point they worked so hard to earn slip away late on, only for Wijnaldum to fire straight at De Gea when picked out in space during stoppage time.