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:
9. Matt O'Riley - 7
Impressed again in a more advanced role. Nice build up play and pressing before Minteh’s disallowed goal. So close to doubling Brighton's lead from close range after Minteh's cutback. Harshly penalised for a handball for Southampton’s penalty. Photo: Ryan Pierse/Getty Images
10. Yankuba Minteh – 9
After seeing one goal ruled out for a foul, the Gambian forward scored two sublime goals which were almost a carbon copy – either side of half time. There was nothing the Saints defenders could do to stop him when he cut in on his left and lined up a shot for the far corner. Could have had another goal to his name earlier but he unselfishly squared it to Kaoru Mitoma – who overran the ball and the chance was gone Photo: Ryan Pierse/Getty Images
11. Georginio Rutter - 7
The Frenchman looked sharp and it was great to see him back in action after his lengthy injury lay-off. He was deployed in the false nine role and lined up well with Minteh and Mitoma. Provided the assist for Minteh's first goal Photo: Ryan Pierse/Getty Images
12. Kaoru Mitoma - 6
It’s so good to see him still in a Brighton shirt after he was heavily linked with a move away. Some lovely first touches, as we have come to expect. Will be disappointed not to have got on the scoresheet, when he overran Minteh’s unselfish cut-back. Photo: Ryan Pierse / Getty Images