The Icelandic international was on hand to convert on the hour following Robert Beric's opener.
Despite enjoying the majority of possession, Maribor failed to carve out any meaningful chances in front of goal in the opening 45 minutes.
Vertonghen should have done better when his header from Tom Huddlestone's cross was easily saved, while Sandro lashed the ball narrowly wide from the edge of the area.
However, the hosts eventually made the breakthrough three minutes before the break when Beric was allowed to slot in from close range.
Maribor began the second half strongly, but it was Spurs who got themselves level as Sigurdsson poked in the rebound after Jermain Defoe's effort was blocked on the line.
Beric came close to regaining the lead for Maribor in the 75th minute when he made a poor connection on Martin Milec's cross, while Vertonghen flashed his shot inches wide late on.