Daniel Akindayini gave Spurs a 38th minute lead but Kieran Bywater whipped in an equaliser direct from a free-kickwide nine minutes after the break.
Tottenham keeper Harry Voss denied the lively Elliot Lee from close before Cristian Ceballos showed great technique to put Spurs back in front on 74 minutes, controlling Milos Veljkovic's ball over the top and slotting home, much to the delight of most of the 794 present.
Spurs: Voss, Fredericks, McQueen, Carroll, Ball, Veljkovic, Sonupe, Winks, Akindayini, Onomah, Celallos
Subs: Oduwa, Glover, Lesniak, Miller, Coulibaly
This is the first of six fixtures for Spurs U21s at Stevenage, with Manchester United U21s next up on Monday 29th September.
Kick-off for all games will be at 7pm on Monday and tickets will be available on the West Stand turnstiles at £5 adults and £2 concessions (over 60 / under 16). Stevenage FC season tickets and loyalty cards will not be valid for these fixtures.
Tottenham U21 Premier League games at The Lamex Stadium (all 7pm KOs)
Monday 29th September - Tottenham U21 v Manchester United U21
Monday 27th October - Tottenham U21 v Chelsea U21
Monday 1st December - Tottenham U21 v Manchester City U21
Monday 5th January - Tottenham U21 v Everton U21
Monday 16th March - Tottenham U21 v Norwich U21