Albion almost staged an incredible comeback from three goals down but Bryan Mbeumo’s second of the night – in the sixth minute of injury-time – made sure of the victory.
The hosts were in charge for 73 minutes, with goals from Matheus Cunha, Casemiro and Mbeumo giving Ruben Amorim’s team a three-goal lead.
But Welbeck’s customary goal against his former team – a classy free-kick – gave the Seagulls hope, with 16 minutes of normal time remaining.
With seven minutes added on, you knew there was time for two more goals. Albion got one of those – with substitute Charalampos Kostoulas scoring his first in Brighton colours.
The Greek striker nodded in at the near post from James Milner’s corner – setting up a grandstand finish.
But Mbeumo extinguished any hopes of a sensational comeback with a powerful strike into the roof of the net. It was virtually the last kick of the game.
The match was not without its controversies. There was a big first-half penalty appeal, before the opening goal, when Amad went down under a challenge from Maxim De Cuyper. Play was allowed to continue and it did not impact the hosts’ momentum.
Fabian Hurzeler will no doubt be furious with two controversial decisions against his team, though. Rutter was adamant he was fouled by Luke Shaw in the build-up the third United goal.
And then, referee Anthony Taylor decided not to send Patrick Dorgu off, after he brought down Minteh on the edge of the box – as the Brighton man looked to be through on goal. Albion scored free-kick, anyway, but Hurzeler will argue they should have been up against ten men for the remaining 23 minutes.
The result leaves United fourth in the table, whilst Albion slip to 12th.
13. Tommy Watson - 7
Really lively off the bench. His pass led to the free-kick, which Welbeck scored. Some lovely touches. He deserves a start sooner or later. Photo: Mike Hewitt/Getty Images
14. Diego Gomez - 7
Thankfully his injuries were not too bad and he came on to help his team on the hour mark. Really lively and helped Brighton in their late resurgence. Photo: OLI SCARFF/AFP via Getty Images
15. James Milner - 7
Brighton's set pieces were mostly poor but on stepped the veteran who showed how it's done. Well taken corner headed in by Kostoulas at the front post. Milner did well to steady the ship and keep things simple. Photo: OLI SCARFF/AFP via Getty Images
16. Charalampos Kostoulas - 8
We've barely seen him in a Brighton shirt but this goal will do him the world of good. Fine header. The youngster protects the ball well when he has it. Photo: Shaun Botterill/Getty Images