Karou Mitoma opened the scoring with a diving header in the first half but Flynn Downes levelled 15 minutes into the second period for Saints.
Archer believed he had put Saints ahead with less than 20 minutes to play before they fell on the wrong side of another controversial VAR decision.
Adam Armstrong was adjudged to have been offside when he interfered with a Ryan Fraser cross, who made a strong impact from the bench.
Brighton hit the woodwork in the final minute as Saints avoided a 10th league loss in a row on the road for first time they endured such a run since the 1973/74 season.
But Downes, Taylor Harwood-Bellis and Tyler Dibling will join Russell Martin's army of unavailable soldiers for the next match after picking up their fifth yellow cards.
Martin made three enforced changes and four in total to his Saints lineup at Brighton with Paul Onuachu, Adam Lallana, Alex McCarthy and Fraser dropping out.
The latter two were named on the bench but goalkeeper McCarthy was not fit to start after taking painkilling injections to get through a knee injury against Liverpool.
It meant a [Premier League](/sport/football/premier_league/) debut for 29 year old Joe Lumley, who had previously been limited to cup appearances since signing for Saints last summer.
Mitoma had the first chance of the match when he picked the pocket of compatriot Yukinari Sugawara, but the Japanese shanked his effort wide.
Downes was then yellow carded for the fifth time this season after tripping Danny Welbeck, meaning he will miss the visit of Chelsea on Wednesday.
Georginio Rutter was kept quiet three times as a Leeds United player last season but nearly opened the scoring with a vicious strike off the outside of the post.
But Saints were unable to make it to the 30th minute with the score at 0-0, as Mitoma ran off Sugawara to head Tariq Lamptey's deep cross past Lumley.
Martin's side had lost all eight Premier League matches in which they conceded first this season while their last win was at Everton in January 2023.
Sugawara looked to atone and set up Archer for the first Saints chance of the first half but the striker - who may have been offside - missed from close range.
Martin opted against any changes at the break and much of the same performance continued before Harwood-Bellis joined Downes in the book.
But against all the odds, Downes fired through a crowd from the edge of the area after Adam Armstrong's blocked shot to level proceedings in the 59th minute.
The goalscorer was finally withdrawn by Martin in the 66th minute after no fewer than five fouls, leaving the hosts incensed that he had not been given his marching orders.
Fraser made an immediate impact when he crossed for Archer to put Saints ahead at the back-post but it was controversially ruled out for offside.
A VAR check confirmed Archer was in an onside position but the offence was given against Armstrong, who jumped over the ball as the cross came in.
The length of that check meant 10 minutes were added on with the game finely poised at 1-1 when Simon Adingra's stretching effort came off Lumley's post.
**Saints**: Lumley; Sugawara (Fraser, 66), Harwood-Bellis, Stephens, Walker-Peters, Manning; Downes (Aribo, 66), Fernandes; Dibling, Archer (Kamaldeen, 87), Armstrong (Brereton Diaz, 90).
**Unused subs**: McCarthy, Edwards, Wood, Bree, Amo-Ameyaw.
**Booked**: Downes, Walker-Peters, Harwood-Bellis, Martin, Gill, Dibling.
**Brighton**: Verbruggen; Lamptey (Dunk, 72), Igor, van Hecke, Estupinan; Ayari, O'Riley (Wieffer, 72), Rutter (Minteh, 87); Pedro (Adingra, 72), Mitoma, Welbeck (Ferguson, 79).
**Unused subs**: Steele, Enciso, McConville, Slater.
**Booked**: Hurzeler, O'Riley.
**Referee**: Robert Jones.
**VAR**: Jarred Gillet.