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:
13. Substitutes
Harry Howell (pictured) – 6: Replaced Minteh after the second goal and wasn't far away from scoring with an ambitious lob from distance. Very nearly teed up Sima with a cross to the far post. Promising signs from the academy graduate, who made his Premier League debut last season | Andrew Moran – 6: The 21-year-old, who has been given a first-team squad number, could be set for a big season. Some encouraging signs but plenty more to come. | Abdallah Sima – 6: Not far away from getting on the scoresheet after his introduction. His future is uncertain, with reports that Championship club Norwich are considering a bid for the Senegal international, who previously impressed while on loan at Rangers. | Jacob Slater – N/A | Charlie Penman – N/A Photo: Ryan Pierse/Getty Images