Brennan Johnson came off the bench to score for the fifth game in succession as Ange Postecoglou offered Tottenham a glimpse of the future.
The Spurs boss threw four teenagers into the Europa League against Ferencvaros and was rewarded with a second win in the competition.
Pape Matar Sarr gave Postecoglou's team the lead before Johnson came on and scored the second in the closing stages.
Barnabas Varga pulled one back for the Hungarian champions but Tottenham, who hit the woodwork twice, were worth the victory.
Postecoglou's teens were Archie Gray, who spent the first half in central defence before switching to left-back and was wonderfully composed and unruffled in both roles, and Lucas Bergvall in midfield, both 18.
Mikey Moore at 17 was making his first start, initially wide on the right and later on the left. Will Lankshear 19 made his debut up front.
Lankshear, signed for £2million from Sheffield United in 2022, was prolific for Tottenham's Under-21s last season but missed the target with an early chance. Picked out by a cross from Timo Werner, he mistimed a header, and it skidded over.
Moore flickered with promise throughout, causing problems for left-back Cristian Ramirez. He and Lankshear were involved in the opening goal although the crux of it was terrible defending by the home team.
Moore drifted inside with the ball and flicked a pass towards Lankshear who battled with the centre-halves as the ball bounced around in front of goal. Ferencvaros wasted their chances to tidy away the danger and Sarr pounced, darting forward to roll in his second goal of the Europa League campaign.
Until then, Spurs had lived dangerously on a slippery surface, which was soon cutting up underfoot after hours of relentless rain. Ferencvaros had opened with purpose, quick on the turnover always searching to break into the space behind Tottenham's high defensive line.
They created early chances. Centre-forward Varga headed one over, Guglielmo Vicario saved from Adama Traore and there was a goal ruled out for offside when the game was goalless.
Eldar Civic crossed from the left and Varga climbed at the back post to head in, but the flag was up. The VAR took a long hard look. It was very tight and in the end the decision was ruled to be correct because knee was a centimetre or two offside.
Vicario made a fabulous save to foil Varga again before Spurs took the lead midway through the first half and took control.
Pedro Porro almost made it 2-0 before the interval with a low curler with his left foot which fizzed through a crowded penalty area and thumped into the foot of a post.
Without the second, the game remained in the balance. Vicario saved from Matheus Saldanha at one end and Lankshear twice went close at the other, first an effort which looped narrowly over from a Porro corner.
Then he was foiled by a last-ditch tackle by Stefan Gartenmann as he prepared to finish on the break. Werner was again guilty of wasting an excellent chance. Picked out by Moore on the break, Werner opted to go around the keeper but carried the ball too wide to finish, hitting the side-netting from a tight angle.
Postecoglou sent on James Maddison, Brennan Johnson and Dejan Kulusevski in an attempt to secure the game. Johnson rattled the bar with one effort before finding the net off the post with his next and it helped Spurs maintain their winning start in Europe.