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.