Chelsea were held to a 1-1 draw at Southampton as their three-match winning run came to an end.
Southampton took the lead on 17 minutes when Sadio Mane lifted the ball over Thibaut Courtois, but the Blues hit back through an excellent solo Eden Hazard goal in first-half stoppage time.
The Blues pressed for a winner and Saints lost Morgan Schneiderlin to a second yellow card in the final minutes, but they held firm to frustrate Jose Mourinho's men.
That result would have allowed Manchester City to close within a point of the Blues at the top of the table, but they threw away a two-goal lead in a 2-2 draw with Burnley at the Etihad Stadium.
David Silva opened the scoring as he swivelled in the box before slotting home, and Fernandinho doubled their advantage with a stunning strike from the edge of the area.
However, Burnley hit back through George Boyd shortly after the start of the second half, and Ashley Barnes fired them level on 81 minutes as City's run of nine successive wins in all competitions came to a shock end.
Arsenal held on for a 2-1 win over West Ham United that took them level on points with fourth-placed Southampton.
West Ham had the better of the opening 40 minutes at Upton Park, and Alex song saw a goal ruled against his former club, but Santi Cazorla was then tripped in the area and converted the penalty in the 41st to put the visitors ahead. Danny Welbeck doubled the lead three minutes later after a pass from Alex Oxlade-Chamberlain.
West Ham kept pressing after the break and Cheikhou Kouyate pulled one back when he rose above Mathieu Debuchy to head into the net in the 54th minute.
Arsenal had several chances for a third on counterattacks, and then withstood a series of late attacks as they clinched a second successive win.
Hugo Lloris refused to be beaten as Manchester United finished an ignominious 2014 with a goalless draw at Tottenham Hotspur.
Louis van Gaal, who succeeded the sacked David Moyes in the summer, had been hoping to end a fraught year on a high and continue United's bid to regain a Champions League place.
However, the Spurs goalkeeper saved twice from Radamel Falcao as well as from Robin van Persie and Ashley Young while Juan Mata's free kick struck the woodwork as the hosts took a share of the spoils.
Newcastle United ended a run of three straight Premier League defeats as they beat Everton 3-2.
Arouna Kone claimed his first Premier League goal for Everton to open the scoring, but Newcastle levelled on 34 minutes through Papiss Cisse, who had earlier escaped a red card despite an apparent elbow on Seamus Coleman.
Ayoze Perez then gave Newcastle the lead on 51 minutes before Jack Colback extended the home side's lead with his first league goal since his move from Sunderland.
Everton substitute Kevin Mirallas reduced the arrears on 84 minutes to make for a nervy finish, but Newcastle held on for a much-needed win.
Mame Biram Diouf netted a double as Stoke City saw off West Bromwich Albion 2-0 and increased the pressure on boss Alan Irvine.
Diouf slotted home in the 51st minute before a lucky deflection off the Senegal forward from Marko Arnautovic's shot 15 minutes later took the ball past Ben Foster once again.
Crystal Palace caretaker manager Keith Millen was unable to steer his side out of the relegation zone as the Eagles began life after Neil Warnock with a goalless draw at Queens Park Rangers.
Millen, who was asked to be in charge of the game at Loftus Road little over 24 hours before kick-off, would have been pleased with his side's endeavour but a lack of quality at both ends meant neither team were able to carve out a decisive chance.
Aston Villa held Sunderland to a 0-0 draw despite going down to 10 men for the third time in four games.
Fabian Delph became the third Villa player to be sent off this month when he saw red for a late foul on Jordi Gomez early in the second half, but Sunderland failed to cash in on their advantage, although Gomez hit the post with three minutes left.
Leicester City clung on by their fingertips to beat Hull City and claim a first victory in 14 Premier League matches, easing some of the pressure on manager Nigel Pearson and ensuring the Tigers remain mired in the relegation battle.
Both sides finished with 10 men after late red cards for Paul Konchesky and Stephen Quinn, but it was the 32nd-minute strike by Riyad Mahrez that settled matters in the visitors' favour.
The Foxes were at times passengers in a low-quality contest but given their current plight this 1-0 win will taste every bit as good as their previous success -- a headline-grabbing 5-3 over Manchester United in September.
Information from the Press Association and Associated Press was used in this report