The north London side join the likes of Aston Villa and Chelsea in the quarter-finals after triumphing over their French opponents 4-3 on penalties at St Germain en Laye
Shaquile Coulthirst had given Spurs the lead but Alexis Sainrimat equalised in the second half, with neither side able to find a winner after extra time, forcing penalties.
Coulthirst struck 11 minutes before the break to continue his impressive form for the youngsters from White Hart Lane but Sainrimat levelled with a tidy finish for Les Parisiens in the 65th minute.
Neither side could find the killer blow at St Germain en Laye as it drifted towards the dreaded spot-kicks.
Goalkeeper Lawrence Vigouroux was the hero as the former Brentford shot-stopper made the decisive save to ensure Spurs' passage to the last eight.
Tottenham will feature in the quarter-final stage alongside Aston Villa and Chelsea, who beat Ajax and Barcelona respectively to book their place in the next round.