The visitors were in control of the first half, hitting the woodwork through Vincent Janssen, while Leverkusen were in complete command after the break, squandering half a dozen scoring opportunities.
French keeper Lloris repeatedly came to Spurs' rescue in the second half, including saving a Javier Hernandez effort on the line.
The result leaves Tottenham on four points, one behind AS Monaco, who drew 1-1 at CSKA Moscow. Leverkusen are third on three, having yet to win a game, with the Russians last, a point behind.
"We should thank Hugo tonight," said Tottenham coach Mauricio Pochettino. "Hugo's save (from Hernandez) was brilliant. He's one of the best, that is my opinion.
"It was a tough game. In the end I'm pleased with a point. We were better in the first half, they were better in the second."
Tottenham got off to a better start and put the ball in the net after 10 minutes only for Son Heung-min, a former Leverkusen player, to be correctly ruled offside.
The English club, with Eric Dier replacing injured Toby Alderweireld, defended well, shutting out Leverkusen in the first 45 minutes.
Dele Alli should have done better when he charged into the box but headed a fine Kieran Trippier cross wide.
Leverkusen keeper Bernd Leno then rescued his team in the 39th minute, tipping an Erik Lamela shot over the bar after Janssen's header had bounced off the woodwork.
The hosts struggled to break into the box in the first half but three minutes after the break Hernandez, who never scored in his four years with Manchester United against Spurs, thought he had done enough when he fired on goal from three metres out.
But Lloris made a fantastic save on the line with goal-line technology showing the ball was not fully over, leaving the Mexican wondering how he could have missed.
Lloris then denied Charles Aranguiz, parrying his free kick and also making another almost identical from an Admir Mehmedi shot on the hour as Leverkusen overran their opponents.
Stefan Kiessling had the chance to win it for the home team five minutes from time but the ball bounced off his shin.
The teams will meet again in London on Nov. 2
(Reporting by Karolos Grohmann; Editing by Ian Chadband)
