The home side had the better of the opportunities and put in one of their hardest-working performances of the season, but could not find a way past Lawrence Vigouroux in the Spurs goal.
The result moves Saints up to fourth in the Barclays U21 Premier League Elite Group, though they will need third-placed Liverpool to lose their final two games if they are to have a chance of qualifying for the play-offs.
With U21 Coach Martin Hunter absent for the match, his assistant Steve Greaves took charge and made four changes to the side that conceded a three-goal lead in their draw at West Bromwich Albion eight days earlier.
Paulo Gazzaniga returned in goal, while Jordan Turnbull came in for Vegard Forren and Harrison Reed replaced the injured James Ward-Prowse.
Sam Hoskins also came back into the side having returned from a four-month loan spell with League 1 side Stevenage.
Spurs, meanwhile, included Steven Caulker and Tom Carroll in their side, with both players having been on the bench for their first team at the weekend.
It was Hoskins – who scored nine goals for the Under-21s in the first half of the season – who had the game's first chance, but his sixth-minute drive deflected over Vigouroux's goal.
Saints had a big opportunity to open the scoring on 21 minutes when Calum Chambers' deep cross was half-cleared as far as Lloyd Isgrove, but the winger's curling effort ended up just the wrong side of the Spurs crossbar.
There were further half-chances for Isgrove and Spurs winger Kenny McEvoy, before Ryan Fredericks had the visitors' best opening of the first half three minutes before the break, shooting inches over Gazzaniga's goal.
If the first period was somewhat tentative, the second would prove to be anything but.
England Under-21 midfielder Carroll, playing in front of his national team boss Stuart Pearce, tested Gazzaniga with a fierce 49th-minute drive that was excellently tipped over by the Argentinian goalkeeper.
Gazzaniga came to Saints' rescue again 60 seconds later, denying Shaquile Coulthirst after the Spurs frontman had got his head onto Zeki Fryers' left-wing cross.
Hoskins then put the ball in the net on 52 minutes after sneaking between centre-backs Caulker and Grant Hall, but he was correctly flagged offside in doing so.
Recalled defender Turnbull went close soon afterwards when he met Joe Curtis's inswinging corner, but his header looped just over Vigouroux's goal.
What was perhaps Southampton's best chance of the game arrived on 59 minutes when Hoskins centred low across the face of goal but the onrushing Jake Sinclair could not keep his close-range shot down.
Hoskins and Sinclair then both had snap-shots held by Vigouroux, before Coulthirst drew another superb stop from Gazzaniga after sliding to get onto the end of a Fredericks cross.
With just over 20 minutes to go, Greaves brought on Ryan Seager, who scored his first goal for the Under-21s in that draw with the Baggies last Sunday.
And Seager went close to making an almost-immediate impact but his deflected effort was superbly turned away by Vigouroux.
Elite Group leaders Spurs still posed a threat, though, as Coulthirst headed Carroll's 74th-minute free kick at goal only to find Gazzaniga in good form once again.
With time ebbing away, another chance fell Seager's way with ten minutes to go as he slid to get onto Sinclair's deflected cross only to see the ball squirm narrowly wide of the far post.
Southampton continued to pressure their opponents in the final stages, with the impressive Matt Targett going close with an 88th-minute free kick that Vigouroux again managed to tip wide.
In the end, Greaves' side were forced to settle for a draw when they perhaps deserved more against the top under-21 side in the country.
If Saints are to finish in the top three and make the play-off, they now need to win their final game of the Elite Group stage and hope that Liverpool lose their last two.
We host West Ham behind closed doors on Thursday afternoon, while the Reds travel to Arsenal on Friday before facing second-placed Manchester United at Old Trafford next Monday.
Saints U21s: Gazzaniga, Chambers, Stephens (c), Turnbull, Targett, Curtis, Reed, Moore (Seager 69), Sinclair, Hoskins, Isgrove. Subs (not used): Johns (GK), Young, Rowe, Gape.
Spurs U21s team: Vigouroux, Barthram, Hall (c), Caulker, Fryers, Gallifuoco (Nicholson 46), Bentaleb, Carroll, Fredericks (Dombaxe 76), Coulthirst, McEvoy (Michael-Percil 62). Subs (not used): Miles (GK).
Referee: John O'Brien