Rafael Benitez's unhappy start as Chelsea manager continued as his side crumbled to defeat against West Ham, while Manchester City were forced to settle for a point against a dogged Everton side. Arsenal slipped further off the pace as they were beaten at home by Swansea, while Tottenham thrashed Fulham.
Manchester City failed to pile the pressure on title rivals Manchester United as they were held to a 1-1 draw at home to Everton.
City, who lost Aleksandar Kolarov early to a groin injury, fell behind after half-an-hour with the visitors having enjoyed the best of the early exchanges - Marouane Fellaini bundling home the rebound after Joe Hart saved his initial header from Leighton Baines' cross.
However, the Toffees' lead was short-lived as Carlos Tevez levelled from the penalty spot when Fellaini was guilty of pulling back Edin Dzeko from a corner after Tim Howard had saved the Bosnian's low volley.
City stepped on the gas in the second half, but they were unable to make their pressure count as Everton hung on for a hard-earned point, and nearly snatched all three as Hart scrambled to save Nikica Jelavic's free-kick in the dying minutes.
Wayne Rooney answered the goalscoring rallying cry of his manager as Manchester United twice came from behind against Reading to claim an enthralling 4-3 victory and move three points clear at the top of the Premier League.
Sir Alex Ferguson said he wanted to see his striker find the back of the net more often and Rooney responded with two strikes in a thrilling match at the Madejski Stadium, where all seven goals came in a 34-minute spell in the first half.
Hal Robson-Kanu gave Reading an early lead before United hit back with Anderson levelling and Rooney putting them ahead from the spot. Reading stunned the visitors with two quick-fire goals to regain the lead as Adam Le Fondre and Sean Morrison capitalised on lapses in United's defence to both score with close-range headers.
But another effort from Rooney and a neat finish from Robin van Persie saw United take the spoils.
Rafael Benitez remains in search for his first win as Chelsea manager as West Ham came from behind for a 3-1 win at Upton Park.
The Blues found their first goal under the Spaniard's stewardship, Fernando Torres setting up Juan Mata in the first half. Torres, Victor Moses and Mata passed up good chances to double the lead and they were made to pay as Carlton Cole headed West Ham level just past the hour.
Petr Cech made a fine save to thwart Matt Jarvis and Ashley Cole headed off the line to deny Winston Reid, but the Hammers kept probing and Mohamed Diame fired home with four minutes remaining. As Chelsea chased the game, West Ham pounced and Modibo Maiga clinched the points.
Arsenal lost more ground on the leaders after they were stunned 2-0 by Swansea City at Emirates Stadium. Two late strikes from Michu snatched all three points for the Swans, who were the better side for much of the 90 minutes after a tame performance by the Gunners.
Arsenal were nearly punished early on after a sloppy start, and they were relieved when the ball fell to Ashley Williams, who lashed his shot wide.
Wojciech Szczesny made an impressive double save to deny Angel Rangel before captain Thomas Vermaelen was called upon to make a last-ditch tackle to deny Nathan Dyer.
Arsenal showed some signs of hunger in the second half and felt they deserved a penalty as Olivier Giroud tumbled following a challenge from Chico, but Mark Clattenburg felt the defender managed to get a toe on the ball.
Szczesny was called upon once again to deny Dwight Tiendalli, and Swansea were rewarded for their flowing play, Michu playing a one-two with Luke Moore before driving a left-footed strike past Szczesny. The Swans' £2 million summer signing then had his 11th goal of the season, showing real composure to round Szczesny after Dyer dispossessed Carl Jenkinson on the halfway line.
Tottenham moved into the Champions League places after an impressive 3-0 win against Fulham at Craven Cottage.
Clint Dempsey was booed on his return to Craven Cottage, but the former Fulham forward will not be too concerned after two quick-fire goals from Jermain Defoe clinched a convincing victory for Andre Villas-Boas' side.
It was Fulham who enjoyed the better of the early exchanges, Mladen Petric forcing a save from Hugo Lloris after the Croatian made good contact with John Arne Riise's dangerous ball from the left.
But the home side were left to rue their failure to convert their chances, and it was Spurs who took the lead early in the second half. The Cottagers failed to close down Sandro in the midfield, and after carrying the ball goalwards, the Brazilian unleashed a 30-yard bullet which beat Mark Schwarzer at his near post.
Jermain Defoe continued his impressive goalscoring form, netting two goals in the space of five minutes - lashing home from close range after a superb solo run by Gylfi Sigurdsson before collecting Dempsey's through ball to slot the ball past Schwarzer.
Spurs leapfrogged West Bromwich Albion into fourth after the Baggies were beaten 1-0 by Stoke City at the Hawthorns thanks to Dean Whitehead's second-half goal.
A stubborn defensive display from the Potters kept Steve Clarke's side at bay, and after soaking up plenty of pressure, the visitors grabbed all three points after Whitehead steered home Michael Kightly's cross to secure Stoke's first away win in the league since January.
Daniel Agger secured victory for Liverpool as they bounced back from their defeat to Tottenham in midweek with a 1-0 win over Southampton at Anfield. The Reds, who welcomed Lucas Leiva back into the starting XI, hit the woodwork on a number of occasions before Agger nodded home shortly before the break.
Southampton, who have picked up seven points from their last three games, started confidently, Rickie Lambert flashing a 25-yard cracker narrowly wide. Luis Suarez looked to be through on goal after running onto Pepe Reina's long ball, but Jose Fonte scrambled the ball away.
Jonjo Shelvey hit the woodwork before Suarez saw his free-kick clatter the crossbar. But while Suarez was ruing his bad luck, Glen Johnson sent the ball back into the box for Daniel Agger to nod in from ten yards.
Faced with the chance to climb out of the relegation zone, the Saints made a bright start to the second half, but Liverpool looked more likely to add to their lead, although Suarez was guilty of squandering late chances.
Harry Redknapp was given a stark reminder of the challenge facing him at Queens Park Rangers as he saw his side take a point from an entertaining 1-1 draw with Aston Villa at Loftus Road.
In his first home game in charge, Redknapp saw his side fall behind after just eight minutes, as they gave the ball away cheaply, leaving Ashley Westwood to find Brett Holman, whose powerful 25-yard shot beat Rob Green.
Rangers were back on level terms ten minutes later, Jamie Mackie rising highest to nod Samba Diakite's chipped cross into the box past Brad Guzan.
The home side's fragility at the back was all too evident, and Villa soon had the ball in the back of the net again, but Christian Benteke was deemed to be offside when he sent a powerful header past Green from Matt Lowton's cross.
QPR were left to rue a host of missed opportunities, as Shaun Wright-Phillips beat Guzan before hammering a half-volley against the post. Clint Hill's strike rattled the bar in the closing stages, but Redknapp was unable to work his magic and secure QPR's first win of the season.