The Spurs defender nudged the ball over the line after Hugo Lloris had parried Mo Salah's header into his path (90), meaning that with six games remaining Liverpool lead Manchester City by two points, though Pep Guardiola's side do have a game in hand.
Liverpool took the lead through Roberto Firmino's glancing header (16) from Andrew Robertson's superb delivery, but Spurs levelled controversially with 20 minutes left through Lucas Moura's tap in, though replays were inconclusive as to whether the ball was in motion from Harry Kane's free-kick to start the move.
Spurs should have score a second late on as Moussa Sissoko blazed over having found himself through, before Anfield went wild with the sloppy winner on 90 minutes.
Spurs' five-man defence allowed both Liverpool full-backs too much space in the first half, and the hosts' opener came from Robertson's delightful left-wing cross, pinpoint for Firmino's as he glanced past Lloris unmarked from eight yards.
But the nerves were still apparent among Liverpool's players in a first-half littered in loose passes, with Dele Alli striking just over on the half volley from 25 yards to give the hosts a scare.
Sadio Mane was within inches of doubling Liverpool's lead at the other end, curling just wide from 20 yards, before Spurs look to rectify their issues by moving to a back four after the break with Danny Rose pushed into left midfield.
Spurs had their first clear opening after the break as Alisson parried Harry Kane's effort into the path of Christian Eriksen, but his follow up was brilliantly blocked by Trent Alexander-Arnold.The title twist seemingly came with 20 minutes remaining as Kane's quick free-kick found Kieran Trippier on the right, though the ball may have been moving as he struck it.
Trippier found Eriksen, whose mis-hit cross was tapped home by Moura.
Alexander-Arnold then saw a cross-shot tipped over by Lloris, but Spurs should have gone ahead with five minutes remaining as Sissoko struck over with Van Dijk concentrated on Heung-Min Son as the visitors broke two versus one.
Alli then curled inches wide again, but Liverpool got their vital winner in dramatic fashion, their 400th goal and perhaps most vital under Jurgen Klopp.
Alexander-Arnold's ball to the back post was headed towards goal by Salah, and though Lloris got a touch, it was weakly parried into Alderweireld, who couldn't help it from rolling over the line.Attention now turns to Manchester City's game in hand against Cardiff on Wednesday night at the Etihad,