Mauricio Pochettino’s men went to Germany hoping to follow up their win in CSKA Moscow last time out in Europe, but having had the edge in the opening half they found themselves under the cosh for large spells after the interval and can be thankful to goalkeeper Hugo Lloris for ensuring they came away with a share of the spoils.
The point keeps Spurs second in the group, a point behind Monaco, with Leverkusen to come to Wembley next in a fortnight.
Leverkusen started the brighter of the two sides, but Spurs had the ball in the net in the 10th minute when Erik Lamela set Heung Min-Son away and he teed up Vincent Janssen for a tap-in, but the offside flag was up to deny them.
Spurs began to impose themselves on the game and had a great chance to open the scoring in the 27th minute when Kieran Trippier put a lovely cross into the area but Dele Alli sent his close-range header wide of the far post.
Spurs went close again in the 39th minute when Alli saw his effort blocked by Omer Toprak, before Trippier’s ball back in was headed onto the crossbar by Janssen and Lamela’s acrobatic follow-up strike was brilliantly tipped away by Bernd Leno.
Javier Hernandez went close to putting Leverkusen ahead late in the half, but the former Manchester United striker’s low effort from 20 yards dropped just wide of Lloris’ upright.
Hernandez thought he had scored three minutes into the second half, but Lloris somehow prevented his effort from two yards out crossing the line with replays backing the French custodian.
The hosts continued to have the upper hand and Lloris again came to the rescue on 58 minutes when he tipped Charles Aranguiz’s free kick wide of the post, before Danny Rose managed to divert Hernandez's volley over his own crossbar via his head.
Spurs continued to hang on with Lloris again called into action on 63 minutes as he got down low to push away Admir Mehmedi’s strike.
On 73 minutes Lloris was guilty of flapping a cross down to the edge of his own area, but was relieved when Toprak fired over the bar.
Spurs went forward on 81 minutes and Christian Eriksen got down towards the by-line but his cross-shot was parried into the air by Leno before he held on at the second attempt.
Leverkusen continued to press in the final minutes with Jan Vertonghen doing well to hack away a dangerous low cross from Julian Brandt as Spurs held on.