Jake Gallagher and Blaine Hudson put the hosts two goals to the good in the first half before Joe Curtis pulled one back just before the break, only for Doug Bergqvist to restore their advantage on 64 minutes.
Seager was one of three attacking players to come off the bench with just over a quarter-hour remaining, and he made it 3-2 from the spot five minutes from time to ignite hopes of a comeback.
And that revival was complete on 89 minutes as the 17-year-old sent a low drive inside the far post to level matters and round off a dramatic evening in south-east London.
Coach Steve Greaves took charge of the team, which consisted mainly of members of the Development Squad as well as a handful of senior players.
Cody Cropper returned in goal having recovered from the finger injury he suffered during the Under-21s' training camp in the north east, while right-back Matt Young captained the side.
Bevis Mugabi and Jason McCarthy – the regular centre-back partnership for the Under-18s last season – started in the middle of defence, with Matt Targett at left-back.
Steve De Ridder spearheaded a midfield three that also contained Curtis and Corby Moore, while Tadanari Lee – who came off the bench to score the winner for the Under-21s against Eastleigh last Friday – joined Jake Sinclair and Jonathan Forte up front.
Welling had an early chance after seven minutes but midfielder Alex Dyer watched his header from Jake Obersteller's cross drift well wide of Cropper's goal.
The hosts continued their bright start, with Kurtis Guthrie firing into the side-netting after getting past Targett before Ross Lafayette had a shot on the turn saved a minute later.
Striker Lafayette had a good opportunity to open the scoring on 20 minutes but he failed to connect after Guthrie had headed across goal, while defender Bergqvist also failed to take advantage of similar situation soon afterwards.
Saints, meanwhile, were forced into an early change on 20 minutes as Targett limped off to be replaced by Fraser Colmer.
Greaves's team had to wait until the 23rd minute for their first chance, as Moore's sweetly-struck half-volley was tipped over the Welling goal by stopper Lee Butcher.
Instead it was the home side who took a perhaps-deserved lead on 31 minutes as some patient build-up play led to Joe Healy squaring for GALLAGHER to fire beyond Cropper from the edge of the Saints box.
However, the visitors went close to an immediate leveller as Lee found space for a shot inside a packed area only to see his chip acrobatically tipped over by Butcher.
The resultant corner was only half-cleared and the ball was quickly returned into the Wings box and onto the head of McCarthy, but the 17-year-old powered his effort inches wide of the far post.
Welling wide-man Guthrie then had a flicked header from Obersteller's inswinging free-kick go just off target, before the hosts' second arrived five minutes before the break.
Louis Fazakerley's corner from the left bounced around the Saints area, and defender HUDSON was quickest to bundle the ball past Cropper to put Welling comfortably in the driving seat with the interval approaching.
However, Greaves's team halved the deficit excellently on 44 minutes as CURTIS hit a rising left-footed drive that flew past Butcher and into the top corner.
HALF TIME: WELLING UNITED 2-1 SOUTHAMPTON XI
Saints looked to build on their positive end to the first half, going close five minutes after the break as De Ridder surged forward and laid the ball off for Lee, but the Japanese's low drive was parried by Butcher.
Cropper had to be on his toes to prevent Welling restoring their two-goal advantage on 56 minutes after Dyer had run clear, with the American saving well again on the hour after some good skill by substitute Loick Pires.
Meanwhile, at the other end, Saints substitute Dominic Gape looked to have poked the ball past Butcher only for Wings left-back Obersteller to race back and clear before it could find the goal.
Welling did restore their two-goal cushion on 64 minutes, though, as Obersteller's inswinging corner found defender BERGQVIST, who powered an unstoppable header past Cropper.
Greaves made a triple change on 73 minutes, bringing on Seager, Jamal Branker and Omar Rowe for De Ridder, Lee and Forte.
However, despite putting in plenty of effort, Saints initially struggled to make their mark against a dogged Welling side as the clock ran down until the game came back to life five minutes from time.
Some good work from Sinclair on the touchline saw him beat his man only to be tripped inside the area, allowing SEAGER to send Butcher the wrong way from the penalty spot to make it 3-2.
Better was follow a minute from time, though, as Saints pushed forward and the ball broke for last season's top-scoring Under-18 SEAGER, who rifled a low left-footer inside the far post to rescue a draw.
FULL TIME: WELLING UNITED 3-3 SOUTHAMPTON XI
Saints XI team: Cody Cropper, Matt Young (c), Bevis Mugabi, Jason McCarthy, Matt Targett (Fraser Colmer 20), Joe Curtis (Dominic Gape 59), Corby Moore, Steve De Ridder (Jamal Branker 73), Jake Sinclair, Tadanari Lee (Ryan Seager 73), Jonathan Forte (Omar Rowe 73). Unused substitute: Will Britt (GK).
Goals: Curtis (44), Seager (pen 85, 89)
Welling Utd team: Lee Butcher, Louis Fazakerley, Doug Bergqvist, Blaine Hudson (Sam Corne 65), Jack Obersteller (Joe Obersteller 65), Alex Dyer, Lee Clarke (c), Jake Gallagher, Kurtis Guthrie (Loick Pires 46), Ross Lafayette, Joe Healy (Kiernan Hughes-Mason 46). Unused substitute: Jamie Turner (GK).
Goals: Gallagher (31), Hudson (41), Bergqvist (64)