Moussa Sissoko, one of four Newcastle signings from across the English Channel in the January transfer window, scored twice on his home debut to claim a 3-2 victory.
As Newcastle moved further clear of the relegation zone, Chelsea missed a chance to close the gap on second-placed Manchester City, which retains a six-point cushion going into Sunday's match against Liverpool.
And the pressure is being cranked up on Rafa Benitez, whose Chelsea side also drew against relegation-threatened Reading on Wednesday after being held by third-tier club Brentford in the FA Cup on Sunday.
"What I know, what I can see, is the team doing well, working hard, and when we have this advantage we have to manage in a better way," Benitez said.
Floodlight failure halted United's match at Fulham for 10 minutes before halftime, and after the break Wayne Rooney provided the spark with a crisp finish to clinch a 1-0 win.
"They made it difficult for us," Rooney said. "We hit the post and crossbar three times. We had to keep going and believe we could get the goal."
Arsenal won by the same scoreline to go a point behind Tottenham and Everton, who are fourth and fifth respectively.
Everton's pursuit of the fourth Champions League spot was held up by a 3-3 draw against Aston Villa, which missed a chance to climb out of the relegation zone.
Wigan also remains in the danger spots with Villa, although ahead of goal difference, after being held to 2-2 by Southampton.
It was also a frustrating day for bottom-place Queens Park Rangers, which was held to 0-0 by Norwich.
Reading, however, moved two points clear of the bottom three by beating Sunderland 2-1, while West Ham climbed to 10th with a 1-0 victory over Swansea.
In the title race, Chelsea's faint hopes of catching United are even slimmer after collecting just eight points from a possible 18 since the start of 2013.
Chelsea fell behind just before halftime at St. James' Park when Jonas Gutierrez buried a header past Petr Cech after connecting with a cross from Davide Santon
There was a further blow before the break for Chelsea when striker Demba Ba, who left Newcastle last month, was forced off with blood pouring from his nose after being caught by Fabio Coloccini.
Chelsea, though, fought its way back into contention in the 55th minute when Frank Lampard scored his 10th goal of the season with a swerving long-range strike.
Chelsea went in front in the 61st when Ba's replacement, Fernando Torres, set up fellow Spaniard Juan Mata to curl the ball past fellow Tim Krul.
But Sissoko made his mark just seven minutes later, with his first goal since joining from Toulouse coming after Cech parried an effort from former Bordeaux forward Yoan Gouffran.
And Sissoko was on target again in the 90th after exchanging passes with Santon.
"(Sissoko) has just got a strength of character about him," Newcastle manager Alan Pardew said. "And there's a power in his game that we were so desperately searching for all season."
At Craven Cottage, the only goal came in the 79th when Rooney latched onto Jonny Evans' long ball and went through the Fulham defence before curling the ball into the bottom corner of the net.
"We are in a great position but we are not going to get carried away," said Rooney, who has 10 league goals this season.
Arsenal is close to rejoining United in the top four after Lukas Podolski's free kick in the 78th deflected off Stoke's Geoff Cameron.
Arsenal would have climbed above Everton into fifth had it not been for Marouane Fellaini's late equalizer for the Merseyside team against Villa.
Despite Victor Anichebe cancelling out Christian Benteke's opener for Villa at Goodison Park, the visitors went 3-1 up after Gabriel Agbonlahor headed home before the break and Benteke netted again in the second half.
But Fellaini pulled one back in the 69th and headed in the leveler in stoppage time.
It left Villa with just three points from the past eight games.
There was also a 90th-minute goal at Wigan, where Shaun Maloney secured a point against Southampton.
Wigan had led through Gary Caldwell's effort, but Rickie Lambert headed Southampton level and Morgan Schneiderlin looked to have clinched the win for the visitors before Maloney's late intervention.
Reading also left it late — but was rewarded with a much-needed win to stay ahead of Wigan just out of the drop zone.
Jimmy Kebe headed in his second goal in the 85th after Craig Gardner cancelled out the first by equalizing from the penalty spot for Sunderland.
At Loftus Road, Adel Taarabt had a penalty saved in the second half by Norwich goalkeeper Mark Bunn as last-placed QPR endured a fourth consecutive stalemate despite a string of new signings in the team.
At Upton Park, Andy Carroll headed in the second goal of an injury-plagued loan spell from Liverpool at West Ham to see off Swansea.