Kwesi Appiah struck twice for Cambridge in the first half - goals on 10 and 28 minutes - with Jon Obika firing home our response from 20 yards 10 minutes after the break. After a flurry of changes, we pushed late for an equaliser but the League Two side stood firm in front of over 4,000 fans.
We started the match with purpose, zipped the ball around and created the first two chances.
Obika's step over opened the door for Will Miller on nine minutes only for Richard Tait to throw himself in to block.
Seconds later, an even better move as Obika flicked to Miller and he squared for Cristian Ceballos to wrap his foot around the ball from 12 yards but Chris Dunn responded with a fine save to his left.
Play switched straight to the other end though as United opened the scoring. Greg Taylor measured his cross from the left and Appiah aimed a class downward header at goal from six yards, Luke McGee almost kept the ball out but it trickled over the line.
The home side were lifted and after Harrison Dunk hit a dipper just over, Appiah doubled the scoreline with another header, this time planting into the corner from Ryan Donaldson's cross from the right.
We got back on the ball in the latter stages of the half without creating a serious chance until the 42nd minute when Ryan Fredericks' deep cross found Ceballos, who fired into the side-netting from the left angle.
Harry Winks replaced Josh Onomah at the break and we started the second half on the front foot.
Miller timed his run into the area on 49 minutes only to shoot wide but the midfielder was there again five minutes later to set-up our goal. Finding room just outside the box, he slid the ball in to Obika, who spun and rifled home low into the corner.
United missed two golden chances through substitutes Liam Hughes and Delano Sam-Yorke just after the hour and by 70 minutes, Ceballos, Carroll, Fredericks, Veljkovic and Obika had been replaced by Nathan Oduwa, Emmanuel Sonupe, Daniel Akindayini, Aaron McEneff and Dominic Ball.
Oduwa and Filip Lesniak caused problems down the left flank in the final quarter and carved out our final chances.
First, Oduwa hit the left byline before cutting back to Lesniak, whose goalbound shot was blocked by Tom Bonner.
Then three minutes from time, Lesniak delivered a fine cross on the run and it looked like Sonupe was set to slide home the equaliser but Bonner was there again to somehow turn the ball away from goal.
Cambridge United: Dunn; Tait, Bonner, Coulson, Taylor; Donaldson (Chadwick, 73), Champion, Diallo (Hurst, 84), Dunk (Hunt, 76); Cunnington (Sam-Yorke, 55), Appiah (Hughes, 46). Subs (unused): Norris, Austin, Taylor.
Spurs XI: McGee; Fredericks (McEneff, 59), McQueen, Veljkovic (Ball, 62), Lesniak; Carroll (Sonupe, 62); Ceballos (Oduwa, 59), Onomah (Winks, 46), Lameiras, Miller; Obika (Akindayini, 69). Sub (unused): Voss.