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:
5. Jan Paul Van Hecke - 7
Was picked to start amid uncertainty over his Brighton future. The player of the 2024/25 season is arguably the Seagulls' most important player and it’s vital he stays. Had a header well-saved from a corner and he played a superb long ball before the Minteh / Mitoma mix-up. Van Hecke was his usual composed self defensively until the late collapse all round. Booked for his protests after the penalty decision. Photo: Ryan Pierse/Getty Images
6. Maxim De Cuyper – 7
The summer signing was influential in the build-up to the opening goal with a clever pass after a driving run forward. The Belgium international – a replacement for Pervis Estupinan – has previously been praised by Fabian Hurzeler for his creativity. He started to show signs of a dynamic partnership with Kaoru Mitoma on the left flank. The 24-year-old looks a solid signing and should be ready to step straight into the first team. Photo: BRUNO FAHY/BELGA MAG/AFP via Getty Images
7. Yasin Ayari - 8
Almost opened the scoring with a good effort, which was well-saved. Set up Minteh’s second goal after a perfectly-timed sliding challenge to win the ball back. Will be looking to build on an impressive season, where he solidified himself as one of Hurzeler’s favourites. Booked late on. Photo: Ryan Pierse/Getty Images
8. Diego Gomez – 6
Some nice moments and contributed to Brighton’s domination for an hour before things unravelled. Needless booking was his last action of the game – the midfielder was replaced by Andrew Moran Photo: Ryan Pierse/Getty Images