The Cottagers had taken a late lead through Freddy Plumain, but Taïder – who was making his first start at any level after joining on loan from Inter Milan earlier this month – hit a smartly-taken leveller to round off a 1-1 draw.
Technical Director Martin Hunter was able to name a strong side for the game, calling on a number of players who had been involved with Saints’ first team in pre-season.
Taïder was included in the starting XI having been an unused substitute in Sunday’s Barclays Premier League opener at Anfield, while the likes of Paulo Gazzaniga, Jack Stephens, Harrison Reed and Matt Targett were also in the side.
Omar Rowe and Sam McQueen went close with headers inside the opening ten minutes, while Jake Sinclair had a shot saved.
For the visitors, Marcello Trotta smashed a shot over after Ryan Tunnicliffe’s corner had been missed by Stephens, while Taïder flashed a shot wide of the Fulham goal after turning smartly on the edge of the Cottagers’ box.
Hunter was dealt a blow just before the interval when Sinclair suffered a knock, meaning he had to be replaced by Josh Sims.
The substitute almost carved open the Fulham defence just after the break but his cross was stopped in front of goal by visiting captain Jack Grimmer, with Rowe firing wide on the rebound.
Flannigan saw a low shot deflect wide just before the hour mark, while Trotta and Sims then took turns to have efforts of their own saved.
The visitors took a late lead on 78 minutes when the ball was slotted through to wide man Plumain, who duly slotted it beneath Gazzaniga to open the scoring.
But the advantage did not last long, as Jason McCarthy closed down a clearance and found Taïder, who shuffled left and right before slamming past Marek Rodek to level matters.
Saints did have a chance to score a last-gasp winner, but Flannigan’s low shot flew just wide of the far post.
Southampton Under-21s: Paulo Gazzaniga, Niall Mason (Will Wood 79), Jason McCarthy (c), Jack Stephens, Matt Targett, Harry Reed, Jake Flannigan, Saphir Taïder, Jake Sinclair (Josh Sims 40), Sam McQueen, Omar Rowe. Unused substitutes: Cody Cropper (GK), Ryan Seager.
Goal: Taïder (81)
Booking: McQueen (67)
Fulham Under-21s: Marek Rodak, Joshua Passley, Jack Grimmer, Stephen Arthurworrey, Noe Baba (Buomesca Tue Na Bangna 55), Freddy Plumain, Ryan Tunnicliffe, Solomon Sambou (Joshua Smile 68), Lyle Della Verde (Jordan Evans 85), Tom Richards, Marcelo Trotta. Substitutes: Dillon Barnes (GK), Liam Donnelly.
Goal: Plumain (78)
Referee: Declan Ford