A Victor Osimhen double after an early strike from Yunus Akgun was enough to overpower the London club, but the Istanbul side should have scored more as they ended the game with a total of 28 shots.
The game sparked into life just six minutes in as the ball fell to Akgun on the edge of the Spurs box and he lashed home a stunning effort. Less than 15 minutes later, the visitors were level when a fantastic pass from Archie Gray found Brennan Johnson who knocked it into the middle for 19-year-old Will Lankshear to tap in for his first senior goal for Tottenham.
Galatasaray were back on the front foot before long as Osimhen had a goal disallowed in the 30th minute. There was no uncertainty two minutes later when Galatasaray cut through the Spurs defence again and he lashed into the bottom corner to restore the lead. Fraser Forster pulled off an excellent save to deny the Nigeria star afterwards, but he was picking the ball out of his net again when a delicate touch from the forward left the goalkeeper scrambling.
Galatasaray were simply relentless, with Osimhen in particular launching shot after shot at the Spurs goal. Ange Postecoglou's team were scrambling at the back and gifting chances to their Turkish hosts, but miraculously stayed two goals behind.
Things seemed to get even worse when Lankshear was sent off for a clumsy tackle, having been booked less than 10 minutes prior, but they responded magnificently by pulling a goal back through substitute Dominic Solanke.
Spurs managed to take control from a deflated Galatasaray, and it looked like it was all set up for some late Dejan Kulusevski heroics when he caught the goalkeeper off his line from distance, but he missed the target. It was too, little too late for Postecoglou's team as the Turkish champions took the points.