United’s teenage winger Adnan Januzaj celebrated his new five-year contract by creating the game’s opening goal in the 26th minute with a superb through ball for Wayne Rooney.
The England striker’s shot was blocked by Southampton goalkeeper Artur Boruc, but Robin van Persie was on hand to sweep the rebound home.
Both Rooney and Van Persie hit the woodwork thereafter, but the hosts were prevented from recording consecutive victories for the first time in the league this season when a header by Southampton defender Dejan Lovren flicked into the net off Adam Lallana from an 89th-minute corner.
“We had the opportunities to go 2-0 up. They had been knocking on the door, but I thought we would see it out,” said United manager David Moyes.
“But if you don’t defend a corner well enough, there’s always a chance they will score.”
The point kept Mauricio Pochettino’s Southampton in the top four, while United were left in eighth place, eight points adrift of leaders Arsenal.
Jack Wilshere scored his second goal in two games to give Arsenal an 18th-minute lead, volleying home from Olivier Giroud’s flick following a dizzying exchange of passes involving Santi Cazorla.
Mesut Ozil scored his first league goal for the club with a header from a Giroud cross in the 58th minute and although Norwich midfielder Jonathan Howson replied for the visitors, Aaron Ramsey came off the bench to make sure of victory before Ozil added a fourth.
“A few weeks ago we lost our first home game here (against Aston Villa) and it was a difficult time, but we responded well and since then we have been consistent,” said Arsenal manager Arsene Wenger.
“I like the solidarity in the team. Of course we have quality, but it’s how much we maintain that and sustain that that will decide our future.”
Jordon Mutch gave the promoted side a shock 10th-minute lead by lifting the ball over goalkeeper Petr Cech after Chelsea defender David Luiz inexplicably allowed a pass from team-mate Ramires to run past him.
Jose Mourinho’s side equalised in the 33rd minute with an unusual goal that saw Eden Hazard sweep the ball home from close range after Samuel Eto’o had stolen possession from Cardiff goalkeeper David Marshall as he bounced the ball.
Eto’o completed the comeback in the 66th minute, and although Mourinho was sent to the stands for dissent, Oscar and Hazard both found the net in the closing stages.
Cardiff manager Malky Mackay described referee Anthony Taylor’s decision to allow Chelsea’s opening goal to stand as “a horrendous error”.
Liverpool, who trail Chelsea on goal difference, twice came from behind to earn a 2-2 draw at 10-man Newcastle United.
Liverpool captain Steven Gerrard claimed his 100th league goal from the penalty spot shortly before half-time, cancelling out Yohan Cabaye’s long-range opener, after Mapou Yanga-Mbiwa was sent off for a last-man foul on Luis Suarez.
“It’s never easy when you’re playing against 10 men, but I thought some of our play was outstanding today. We had to show character twice, coming from behind,” said Liverpool manager Brendan Rodgers.
“But give Newcastle credit as well. A point at St James Park won’t be the worst result you can get.”
Gus Poyet’s tenure as manager of bottom club Sunderland began in lamentable fashion as his side crashed 4-0 at Swansea City.
All the goals came in the last 33 minutes, with Jonathan De Guzman, Wilfried Bony, from the penalty spot, and Chico Flores netting after recalled Sunderland full-back Phil Bardsley opened the floodgates by putting through his own goal.
Steven Pienaar scored within seconds of coming on to earn Everton a 2-1 victory at home to Hull City, while West Bromwich Albion were held to a 0-0 draw at Stoke City.
The late game sees Manchester City visit West Ham United.