The Premier League side were able to claim a point in Germany, despite Roger Schmidt's men passing up several chances throughout the game
Hugo Lloris was Tottenham's hero as they held Bayer Leverkusen to a 0-0 draw at the BayArena in Tuesday's Champions League clash.
The France goalkeeper made a string of second-half saves - the best of which came against Javier Hernandez - to deny the home side a first win against English opposition since 2011 and keep Group E wide open after three matches.
Son Heung-min, making his first appearance against his old club, set up Vincent Janssen for a first-half tap-in that was ruled out for offside, but it was Spurs who looked the more threatening in a scrappy opening 45 minutes.
Roger Schmidt's side came to life after the break only to be kept at bay by the brilliance of Lloris, with the skipper denying Charles Aranguiz and Admir Mehmedi either side of a stunning reaction stop to keep Hernandez's effort from squirming in.
Omer Toprak came close to finding a winner, but Leverkusen were forced to settle for a third draw in as many group games, with Tottenham a point above them in second place behind Monaco.
It took Son just 10 minutes to make an impact on his return to Germany as he raced through the home defence before squaring for Janssen to tap in, only for the offside flag to rescue Leverkusen.
Spurs enjoyed more possession in the first half-hour of a rain-soaked encounter, with Son looking a real threat when cutting in from the left, but Dele Alli wasted the best chance when he headed Kieran Trippier's teasing cross wide of the post.
The game was interrupted too often by niggling fouls and poor passing, but Tottenham almost snatched the lead when Janssen's header came off the crossbar and Erik Lamela's rebound was tipped over by Bernd Leno.
Hernandez should have given Leverkusen the lead three minutes into the second half. Lars Bender's cross picked out the Mexican at the far post, but he side-footed straight at Lloris from point-blank range, and the Spurs keeper reacted superbly to keep the ball from crossing the line.
Lloris palmed away a low free-kick from Aranguiz, before Danny Rose headed a Hernandez half-volley up and over the crossbar, as Mauricio Pochettino began to pace a little more nervously on the touchline.
Mehmedi was the next to be thwarted as Lloris parried away his low drive from 20 yards, before Stefan Kiessling's strike was tipped wide and Toprak headed the resulting corner straight at the grateful goalkeeper, who received a rousing reception from the Spurs faithful at the final whistle.