After a thrilling three-match series there is nothing to separate the sides, having won one Test apiece and drawn this gripping decider in Auckland.
The All Blacks led 12-6 at the interval and were on course for victory heading into the closing stages, before Farrell found the target from range with three minutes left on the clock.
Beauden Barrett successfully landed the extras to put the back-to-back world champions seven points in front, but Farrell's kicking - a key feature of the game - saw the Lions claw back six points with a little over half an hour played.
Jordie Barrett played a big part in the opener and it was he who found the whitewash to open up the Kiwis' lead once more, cantering into the corner late in the first half.
Moments after the second-half restart the tourists won a penalty for Elliot Daly to boot over, before Farrell did likewise on the hour for his third of the night in Auckland.
Then came a finale befitting the hugely entertaining series, as Beauden Barrett found the sticks with 12 minutes remaining after an error from Kyle Sinckler, putting New Zealand on course for the decisive win.
Referee Romain Poite would award another pen late on for Farrell to write his name in folklore, however, with the hosts being penalised for hanging on inside their own half.
The Lions pushed for a winner in the remaining minutes but it just was not to be, ensuring a subdued atmosphere around Eden Park as both sets of players were left reflecting on a rare drawn series - just the second time that has happened in the Lions' history.