The hosts had a great chance to take the lead with 20 minutes on the clock but Gareth Bale's weak header was easily dealt with by goalkeeper Federico Marchetti after Aaron Lennon had opted to cross instead of shoot.
Clint Dempsey was then unfortunate not to get his first goal for the club when his header was ruled out for offside. However, the American looked to have been played on by Lulic.
The closest either side came to a goal came in the first half was in the dying moments when Alvaro Gonzalez saw his stinging volley come back off the crossbar after Spurs had failed to clear their lines from a corner.
There was a scramble in the Lazio area at the start of the second period but Lennon and Dempsey were both denied by a stubborn Italian defence.
Sandro was then guilty of wasting a great opportunity to give Spurs the lead.
Bale whipped in a free kick from the left that the visiting defence struggled to deal with, but the midfielder somehow put his header wide from close range.
There was a late scare for Spurs when debutant Hugo Lloris, who had looked solid for most of the night, failed to deal with a cross, but Jan Vertonghen was on hand to clear.