The Saints keeper had not played since suffering a serious knee injury against Burnley in March last year, but he made a string of superb saves to go along with Ryan Seager’s match-winning strike.
The pick of the bunch was a stunning second-half stop, as he stuck out his left foot to flick a low shot destined for the far corner onto the post and away.
Saints now advance to the last 16 of the competition, where they will host Huddersfield.
Six of the side who started both legs of last year’s final against Blackburn were in the line-up for this clash, as Technical Director Martin Hunter fielded a strong team, which featured centre-half Jack Stephens following his recall from a loan spell at Middlesbrough.
It was the visitors who made the better start, though, as their probing attack put the cup holders under pressure in the early stages.
Charly Musonda had the first effort, on six minutes, but he fired a first-time strike from 20 yards over the bar.
Forster was then called into action ten minutes later, making a good diving save to his left to keep out Tammy Abraham’s header. The rebound fell kindly to Reece Mitchell, but Stephens got across to make a brilliant block.
Seconds later, Alfie Jones superbly threw himself in the way of a Palmer shot, diverting it just wide, as Saints continued to resist.
Hunter’s men then started to come into it, with Josh Sims’s sublime turn and cross in the 19th minute hitting Blues defender Joseph Colley. The hosts appealed for a handball, but referee Steven Plane saw nothing untoward.
McQueen then had a chance from 18 yards, but couldn’t connect as the ball dropped out of the air, before Saints’ best chance of the half fell to Hesketh ten minutes before the break. He received the ball just inside the area from a Seager pass and shifted the ball nicely onto his left foot, but put his low shot just wide of the near post.
Saints, who made one change at the break with Josh Debayo replacing Matt Targett, nearly led within three minutes of the restart, as McQueen got free down the right and sprinted in on goal, only to curl his left-foot shot towards the far corner just over.
It mattered not, however, as the hosts did break the deadlock with a fantastic Seager goal in the 52nd minute. The striker took a Harry Reed pass on the edge of the area, turned two Chelsea defenders to get clear, then rounded keeper Bradley Collins before slotting into the net.
Chelsea responded and substitute Alex Kiwomya crossed superbly for Palmer, only for him to side-foot wide of the post in the 63rd minute.
Shortly afterwards, Palmer was then denied by a stunning Forster stop. The Chelsea man worked space in the area and sent a low, left foot shot towards the far corner from close range. It looked destined to be a goal, but the Saints keeper got a touch with his left foot to flick it onto the post and away.
Chelsea continued to push and perhaps should have leveled when Abraham latched onto a Kiwomya cross, but he side-footed over from a dangerous position.
With nine minutes left, Forster again denied the Blues, turning Musonda’s low shot wide after the ball fell to him from Mitchell’s left-wing cross. And when he was beaten in the 90th minute by Abraham, latching onto a teasing cross at the back post, Jones was there to clear off the line and keep the clean sheet intact.
Southampton Under-21s (4-2-3-1): Fraser Forster; Dom Gape, Alfie Jones, Jack Stephens, Matt Targett (Josh Debayo 46); Harrison Reed, Armani Little; Sam McQueen (Olufela Olomola 85), Jake Hesketh, Josh Sims; Ryan Seager.
Unused substitutes: Harry Lewis (GK), Thomas O’Connor, Tyreke Johnson.
Goal: Seager (52).
Chelsea Under-21s (4-2-3-1): Bradley Collins; Fikayo Tomori, Joseph Colley, Jake Clarke-Salter, Kevin Wright; Mukhtar Ali (Alex Kiwomya 61), Charlie Colkett; Reece Mitchell (Isaac Christie Davies 83), Kasey Palmer, Charly Musonda; Tammy Abraham.
Unused substitutes: Jared Thompson (GK), Josimar Quintero, Ali Suljic.