Goals from Thierry Rohart-Brown and Nick Oyekunle looked like they would be enough to move Adam Lallana’s charges up to second in the Premier League 2.
Yet Reece Welch’s 91st minute equaliser prevented the hosts from moving within a point of top spot in the division’s only early kick-off
Having drawn two of their last three games, Saints knew a win would boost their chances of an easier play-off draw, with only four games left to rack up points.
They started slowly, and it was the Toffees who took the lead on 10 minutes when Demi Akarakiri punished sloppy possession.
Recent first-team debutant Sufianu Sillah Dibaga went close with a bending effort before Saints levelled with a slick team move.
Rohart-Brown, scoring for the second time in three games, powered past the Everton goalkeeper after he was played in by Harry Gathercole.
Oyekunle, having shaken off a knock in the first half, completed the comeback by nodding in from close range to hit his ninth of the season.
But Saints could not hold on to all three points and were dealt a hammer blow when Welch headed in from a corner at the death.
They then needed Joachim Kayi Sanda to produce a slide tackle inside the box to stop Everton claiming a last-gasp victory at Staplewood.
Saints: Fisher, Okunola (Adeji-Afriyie, h-t), Dobson-Ventura, Kayi Sanda, Sesay, Williams, O’Brien-Whitmarsh (Daley, 71’), Rohart-Brown, Gathercole (Charles, 71’), Sillah Dibaga, Oyekunle.
Unused subs: Moore, Kakay.
Everton: Lukjanciks, Samuels-Smith, van Schoor, Welch, Thomas, Bates (Olayiwola, 56’), Boakye (Loney, 76’,) Gomez, Ebere (Pita, 76’), Akarakiri, Graham.
Unused subs: Patrick, Davis.