Chelsea took advantage of a late defensive blunder to beat Manchester City as Tottenham saw off Hull and Sunderland won the Wear-Tyne derby.
Fernando Torres scored an injury-time winner as Chelsea beat Manchester City 2-1 at Stamford Bridge.
A stunning goal from Sergio Aguero looked to have earned the visitors a point after Andre Schuerrle had given his side a first-half lead.
Schuerrle tapped in from close range after excellent work from Torres, who collected the ball on the right-hand side before beating Gael Clichy for pace and putting in an inch-perfect cross for his German strike partner.
And Torres would have the last word as a late defensive mix-up between Joe Hart and Matija Nastasic allowed him to tap home and secure the three points.
For the third time this season Tottenham Hotspur earned a 1-0 victory thanks to a Roberto Soldado penalty, as Hull City left White Hart Lane with nothing to show for their efforts.
Spurs broke the deadlock 10 minutes from time when Ahmed Elmohamady was adjudged to have handled Jan Vertonghen's cross in the area. Soldado sent Harper the wrong way from the spot for his fourth Premier League goal of the season.
The win was enough to move Spurs into the top four on 19 points, while Hull drop to 10th, behind Swansea, who played out a 0-0 draw with West Ham.
The Hammers created more chances at a rain-drenched Liberty Stadium with Stewart Downing forcing saves from Michel Vorm, while Ravel Morrison also went close when he fired wide from 10 yards.
At the other end, Jussi Jaaskelainen made two decent blocks to deny Chico Flores and Wilfried Bony.
Fabio Borini wrote himself into Wearside folklore as he came off the bench to fire Sunderland to a 2-1 derby victory over Newcastle and lift them from the foot of the Premier League table.
Borini, signed on loan from Liverpool, struck with an 85th-minute piledriver to secure just a second home league win for the Black Cats over their neighbours since 1980 and a first in the league this season.
His intervention came as Newcastle looked for a winner of their own after Mathieu Debuchy had dragged them back into the game with a 57th-minute equaliser, his first goal for the club.
Steven Fletcher had headed the home side in front with just five minutes gone as Gus Poyet's men made light of their recent difficulties in his first home game at the helm in front of a crowd of 46,313.