Harry Kane and Son Heung-min have now assisted one another to score 50 times for Spurs in all competitions
Frankfurt took an early lead when Eric Dier lost possession and Daichi Kamada was teed up to score from close range but Harry Kane set up Son for the equaliser six minutes later.
England captain Kane then scored from the penalty spot and Son's thumping volley made it 3-1 before half-time.
Frankfurt's Tuta was shown a second yellow card for bringing Son down early in the second half but Faride Alidou's header made it 3-2 with three minutes remaining to make for a nervous ending for Spurs.
Kane missed a second penalty in stoppage time but Tottenham held on for a deserved win.
Tottenham looked back to their best at times and could have won by a greater margin, but sloppy mistakes kept Frankfurt in the game.
The visitors largely struggled to deal with Spurs' attack but goalkeeper Hugo Lloris was forced to tip over an effort by Jesper Lindstrom and there was some desperate defending as Frankfurt had chances late on.
Antonio Conte's hosts threatened throughout with Son, Ryan Sessegnon, Richarlison and Cristian Romero among those to come close.
It was a frantic finale but victory means Tottenham sit top of the group with two wins from four matches, while Frankfurt drop to the bottom of the table with four points.
Tottenham next host Sporting Lisbon on 26 October.
Son Heung-min scored his fifth Champions League brace
Frankfurt dominated early on and pressed and harried Spurs, leading to a mistake from Dier and the opening goal from Kamada, who had already come close when just failing to connect with Lindstrom's curling cross.
But it did not take long for Tottenham to capitalise on the gaping spaces left in behind by Frankfurt.
Kane and Son were on form, linking up fluently and causing havoc as Richarlison worked tirelessly to create space for his team-mates to run into.
The efficiency of Spurs' attacking line-up was too much for Frankfurt and it was only a matter of time before the hosts turned things around.
Kane won and converted a penalty when he was bundled over in the box by Kristijan Jakic less than 10 minutes after he had set up Son for the equaliser.
Son, who came off to a standing ovation, capped off a superb performance with a thumping volley before half-time.
Kane and Son have now linked up 50 times to score for Tottenham in all competitions and Richarlison's addition to the squad has added further attacking threat.
The Brazilian almost set up Sessegnon with a brilliant curling cross early in the second half and was unfortunate not to score when he headed inches wide in the opening period.
Tottenham should have finished with a comfortable victory but the late header from Alidou gave way a wild few minutes as Spurs substitute Bryan Gil missed a diving header, was then fouled in the box to earn a penalty and Kane uncharacteristically fired it over the bar.
The crowd roared with urgency as Tottenham threw bodies in front of the ball to block a late onslaught from the visitors but they hung on to claim victory.
It was a positive night for Tottenham overall as they also welcomed the return of Lucas Moura, who came on as a substitute for his first appearance since August due to injury.
-- Courtesy of BBC Sport