Arsenal stayed top of the Premier League after scoring two late goals in a 2-0 win over Cardiff while fellow title rivals Manchester City, Chelsea and Liverpool also started the year with victories on Wednesday.
However, the league trophy looks more out of reach than ever for Manchester United after the reigning champions lost 2-1 at home to Tottenham and fell 11 points behind Arsenal.
Nicklas Bendtner and Theo Walcott scored Arsenal's goals at Emirates Stadium to beat a resilient Cardiff team which played in front of expected new manager Ole Gunnar Solskjaer and frustrated the hosts for 88 minutes in the driving rain.
"We have a special spirit in the side and you know we'll fight until the last minute in the game," Arsenal manager Arsene Wenger said.
City remained a point behind in second after a 3-2 win at Swansea, while Chelsea's 3-0 victory at Southampton in awful weather conditions ensured Jose Mourinho's team stayed in third place, two points behind the leaders.
After two consecutive losses, Liverpool climbed back into the top four after Luis Suarez scored his 20th goal of the season in a 2-0 win over Hull.
Spurs climbed above United into sixth place — two points behind Liverpool — after goals by Emmanuel Adebayor and Christian Eriksen earned them a second straight league win at Old Trafford. United has now lost four times at home this season.
Arsenal had to wait until two minutes from time before Bendtner gave the Gunners reasons to celebrate the start of a new year when he pounced from a rebound. The striker picked up an ankle injury while scoring and was substituted before Walcott chipped the ball over goalkeeper David Marshall.
"He was a bit unlucky, he said he landed on the foot of a Cardiff player and sprained his ankle," Wenger said. "It looks like it is not a question of days, but weeks."
In other games, Everton fell to fifth by being held 1-1 draw by Stoke, Aston Villa beat last-place Sunderland 1-0, Fulham earned a comeback 2-1 win over West Ham to climb out of the relegation zone, Crystal Palace drew 1-1 with Norwich and West Bromwich Albion beat Newcastle 1-0.
Man City carried its recent form into 2014 and recorded the first goal of the year after 14 minutes when Fernandinho gave Manuel Pellegrini's team the lead at Liberty Stadium. Wilfried Bony put the hosts back in the game with a header but City was more clinical after the interval and pulled away with goals from Yaya Toure and Aleksandar Kolarov before Bony pulled another one back.
Fernando Torres helped Chelsea to a 3-0 victory over Southampton as the Blues kept pace with their rivals. The Spain striker broke the deadlock on the hour mark, heading home a deflected cross from close range. Chelsea's substitutes then combined to deliver the second, with Oscar cutting in from the left to set up Willian for a powerful shot from the edge of the area in the 71st minute.
Oscar then put the result beyond doubt with a clinical finish in the 82nd minute after Eden Hazard and Ramires linked up to put the Brazilian through.
Suarez set a Premier League record when he scored his 20th Premier League goal in just 15 games after missing five matches with a suspension. He doubled the Reds' lead in the 50th minute with a perfect free kick curled into the top left corner after Daniel Agger had headed home Philippe Coutinho's corner to make it 1-0 in the 36th.
"It was our best win of the season," said Liverpool manager Brendan Rodgers. "After a tough period, to get a result like that against a very good team."
Liverpool captain Steven Gerrard made his return off the bench to play his first game since picking up a hamstring injury in early December.
The other Liverpool club, Everton, had a less enjoyable day. Leighton Baines converted an injury-time penalty to earn his side a draw that could not prevent it from slipping to fifth.
Everton enjoyed plenty of possession and hit the woodwork twice in the first half before Oussama Assaidi gave Stoke a 49th minute lead against the run of play.
The visitors were rewarded for all their pressure at the very end, though, when Jermaine Pennant fouled Leon Osman and Baines made no mistake with the spot kick.
Aston Villa ended its five-match winless run by beating Sunderland and goals from Steve Sidwell and Dimitar Berbatov helped Fulham defeat 10-man West Ham.
Saido Berahino converted an 87th-minute penalty to secure the win for West Brom, overshadowing the return of Nicolas Anelka after his controversial goal celebration. Newcastle looked like holding on for a draw despite the 62nd-minute sending-off of defender Mathieu Debuchy for a two-footed tackle on Claudio Yacob, only for goalkeeper Tim Krul to trip Matej Vydra in the area.
Berahino, a halftime substitute, slotted the penalty into the corner for the win.
Anelka started despite being the subject of a league investigation for celebrating a goal against West Ham on Saturday with a gesture that has anti-Semitic connotations.