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 2-2 Brighton
Yankuba Minteh scored twice but Brighton let a commanding lead slip, in their penultimate pre-season friendly, against Southampton. Photo: Ryan Pierse/Getty Images

2. Jason Steele – 8
Got his chance to impress, with Bart Verbruggen still yet to feature in pre-season as he recovers from a knee injury. Steele was excellent with his feet today and he was quick off his line when called upon. Three or four times his play out from the back sent the Seagulls flying forward. Not much he could have done about either of the goals. Photo: Eddie Keogh/Getty Images

3. Matts Wieffer - 6
Worked hard in the right-back role and offered an outlet going forward. Needed to take better care of the ball when Southampton were piling on the pressure. Didn’t cover himself in glory defensively late on. Right back is not his favoured position but there were signs he can make the position his own with time Photo: Ryan Pierse/Getty Images

4. Lewis Dunk – 7
Will be looking to improve on a rocky season. He was clearly full of confidence, evidenced by his audacious effort from the half way line, which landed onto the roof of the net. The skipper was mostly solid defensively until his unfortunate deflection led to Southampton’s comeback. He struggled to restore control of the defence as the Saints threatened to find a winner Photo: Ryan Pierse/Getty Images
