The England worldwide had found the net in the first half too, his deflected drive making it 2-1 after Pierre-Emerick Aubameyang's poked finish had cancelled out Shane Long's early opener for the visitors.
In a wild last few minutes Mohamed Elneny and Southampton's Jack Stephens were sent off in separate incidents.
The result was an attack with less playmaking ability but a lot more pace, and they always looked a lot more risky on quick counters than when trying to orchestrate the normal slow build-up moves.More news: IPL 2018, Kolkata Knight Riders vs Royal Challengers Bangalore, Match Preview
Cedric's cross appeared easy for Arsenal to deal with, yet a mix-up between Shkodran Mustafi and Petr Cech allowed the alert Long to squeeze ahead of the former and stab the ball in from close range.
The game was dominated by neither side, as both teams had their fair share of assertiveness.
In Sunday's other league game, Javier "Chicharito" Hernandez scored minutes after coming on as a substitute to earn West Ham a 1-1 draw at Chelsea in their London derby.
Another England World Cup hopeful was heavily involved as the injury-ravaged Welbeck netted his first league goals since September.More news: Yankees bounce back to ground Orioles
He offered further proof of that here as he put away the only chance his teammates created for him in the first half, pouncing on clever backheel flick from Welbeck to poke the ball past Alex McCarthy.
Having put CSKA Moscow to the sword on Thursday, winning the first leg of the Europa League quarter-final 4-1, Arsenal made heavy weather of seeing off a side sitting in the Premier League's relegation zone.
Danny Welbeck looked keen to add to his tally, but he missed an open goal initially. Towards the start, the Saints had the edge, and it looked like it was going to be another one of those days for Arsenal.
Playing at home for a fifth successive outing, Arsene Wenger's side eventually prevailed in a see-saw contest to record their 150th league victory at the Emirates Stadium. It wasn't for a want of trying, though.More news: Fire at Trump Tower, 1 injured
They had a bit of bad luck as well, as Long thought he had made it 2-2 but had his effort ruled out for offside.