In a busy first half, two well taken goals from Son Heung Min either side of a Harry Kane penalty calmed the home fans after Europa League champions Frankfurt had taken an early lead through Daichi Kamada.
Any hopes of a Frankfurt comeback were dashed on the hour mark when they were reduced to 10 men after defender Tuta was sent off for his second booking in a matter of minutes after twice bringing down Son on the left wing.
The German side did spook the hosts with three minutes remaining when Faride Alidou rose highest from an inswinging corner to head the ball down and in. But even with Kane missing another penalty, Spurs held on.
The win put Antonio Conte's side top of Group D on seven points. However, it is still all to play for as Marseille and Sporting are tied on six points, and Frankfurt remain in the hunt on four with two games left to play.
"Everything is in our hands, we have the possibility in the next game to go through which would be a big achievement because this is our target for the season, to get to the next stage of Champions League," Conte told a news conference.
Spurs were held 0-0 at Frankfurt last week and the visitors started fast, their pressure paying off in the 14th minute when Tottenham defender Eric Dier lost control of the ball and Sebastian Rode squared it for Kamada to stroke in from close range.
Their joy was cut short six minutes later when Kane turned expertly during a Spurs counter-attack and played the ball through to Son who sprinted on goal, took two touches and side-footed past goalkeeper Kevin Trapp.
The equaliser also sparked Spurs into life, particularly Kane who burst forward in the 27th minute, riding three challenges before being barged over by midfielder Kristijan Jakic.
Initially, the referee waved away appeals for a penalty but after being referred to view the incident on the pitchside monitor, pointed to the spot from which Kane coolly converted for his 257th goal in all competitions for the club.
Spurs made it 3-1 in the 36th minute when midfielder Pierre-Emile Hojbjerg ran to the byline and floated in a cross for Son who struck the ball beautifully with his left foot into the roof of the net.
The South Korean could have had a hat-trick before halftime, but his angled effort was stopped by the outstretched boot of Trapp.
Son still tormented Frankfurt's defence after the break, resulting in Tuta being shown a red card for twice bringing down the forward in the space of three minutes.
Just when the game was petering out, Frankfurt scored a second from a corner when Alidou rose highest to head in.
Kane had the chance to seal the win from the penalty spot after substitute Bryan Gil had been tripped in the box in the first minute of stoppage time.
He blasted his effort over the bar and Frankfurt pressed forward but Spurs held out for their first win in the competition since beating Marseille last month.
Conte was not happy with how Spurs finished the game.
"The teaching has to be that no one has to consider the game ended," he said. "Now we are talking with a smile because we won but imagine if we finished with a draw. That would have been a disaster."
Spurs can seal their place in the round of 16 for the first time in three years when they host Sporting on Oct. 26 and Frankfurt entertain Marseille.