Rutter and Mitoma both went close in the early stages for the visitors before Yankuba Minteh somehow failed to take advantage when played through on goal – seeming to stumble as he lined up his shot.
It did not take long for Albion to conjure up another one-on-one opportunity, with the returning Pedro lifting a delightful chip over the on-rushing Aaron Ramsdale.
The Seagulls were unable to add to their lead before the half-time whistle, and it looked like they might be made to regret that when Cameron Archer put the ball past Bart Verbruggen early in the second-half – but the offside flag was up.
Fabian Hurzeler’s side took full advantage of that reprieve and doubled their lead before the hour mark.
It was the lively Rutter who found the net after an unselfish cutback by Minteh, as Southampton were made to pay for a characteristic poor error when playing out from the back. There were shouts for a foul but Rutter won the ball fairly before the goal.
Minteh once again failed to take a golden chance after doing so well to sit Ramsdale and Kyle Walker-Peters down, and leave the goal wide open – but he delayed his shot too long.
But it was soon 3-0 anyway, with Mitoma scoring his fifth goal in the last seven games. It was a lovely finish after being played in by Pedro – but was far too easy from a Southampton point of view.
The Seagulls were not done there – with Hinshelwood grabbing a fourth goal from close range after Southampton failed to deal with a corner.
It was a near-perfect performance from Brighton, who made it three wins on the bounce and confidence is flowing again.
They move up to eighth and sit just four points below fourth-placed Manchester City, who face Liverpool on Sunday.
Here are our player ratings:

1. Southampton 0-4 Brighton
Joao Pedro, Georginio Rutter, Kaoru Mitoma and Jack Hinshelwood all got on the scoresheet as Brighton comfortably beat Southampton 4-0 and earned their third successive win in all competitions. Photo: Steve Bardens/Getty Images

2. Bart Verbruggen - 7
Good save at full stretch after 37 minutes – his first meaningful action of the game. Had little else to do, in truth. Photo: Steve Bardens / Getty Images

3. Tariq Lamptey - 7
Did his jobs defensively and offered a threat going forward. Photo: Steve Bardens / Getty Images

4. Adam Webster - 7
Really impressive so far this season and it was another solid afternoon for the veteran defender. Photo: Mike Hewitt / Getty Images