United, who started the day four points adrift of Chelsea, ended it just a point behind with three matches remaining and everything to play for after beating Manchester City 1-0 with a last-gasp goal from Paul Scholes.
Chelsea, reduced to 10 men after captain John Terry was sent off in the 66th minute for a second yellow card, remain on 77 points while United closed in with 76.
Jermain Defoe opened the scoring for Spurs at White Hart Lane with a 15th minute penalty after a handball by Chelsea captain John Terry, whose nightmare evening ended when he collected a second yellow card.
Gareth Bale had hammered in Tottenham's second goal just before half time with a low shot past Petr Cech at the near post that left the visitors reeling.
As the clock ticked towards 90 minutes, 10-man Chelsea were lucky not to have conceded more goals as Spurs fans began to celebrate - only for the chants of 'Ole' to stick in their throats when Frank Lampard pulled a goal back in stoppage time.
But Chelsea's response came too late to affect the outcome.
SCHOLES GOAL
"We well deserved the win tonight, there's no doubt about that," Tottenham manager Harry Redknapp told ESPN television. "I thought we were even better today than we were against Arsenal.
"That first 30 minutes or so we completely dominated and then we had some great chances in the second half.
"We missed three or four unbelievable opportunities to really kill them off completely."
Chelsea manager Carlo Ancelotti, who will be without Terry for their next match at home to Stoke City on April 25, agreed his men were outplayed but saw no reason to panic.
"We were a little bit down but this is football," said the Italian. "The title is still in our hands, we don't have to be afraid. We have to stay calm and look at the next game."
While United manager Sir Alex Ferguson will doubtless ring Redknapp to thank him for services rendered, the feeling will be mutual. Spurs had plenty of motivation of their own in a lively and at times hot-tempered game.
Fighting for the final Champions League qualifying slot after beating north London rivals Arsenal 2-1 on Wednesday, Tottenham's victory moved them into the coveted fourth place on 64 points and ahead of Manchester City on 62.
LAMPARD VOLLEY
Chelsea, with injured England defender Ashley Cole back on the bench and national team manager Fabio Capello watching from the stands, had a Lampard volley saved by Brazilian Heurelho Gomes just before half time.
Their problems deepened when Didier Drogba appeared to pull a muscle just before the restart with Chelsea having already used all of their substitutes.
While the striker soldiered on, Terry's departure left Chelsea fighting for breath as Defoe repeatedly ripped through the defence in a win that was far more convincing than the scoreline suggested.
