Gylfi Sigurdsson rescued what may prove to be a vital point for Andre Villas-Boas' side with a 58th-minute goal to cancel out Robert Beric's opener.
Spurs looked comfortable but rarely threatened Maribor goalkeeper Jasmin Handanovic for much of a quiet first half.
Ales Mejac sliced a long-range effort wide for the home side who also offered little in attack until they snatched the lead in the 42nd minute.
Dejan Mezga surged into the area on the left and beat both Kyle Walker and Tom Huddlestone before squareing for Beric to poke home.
Villas-Boas brought on Iago Falque at the break and the Spaniard played a key role in the equaliser when his centre was palmed out by Handanovic.
Jermain Defoe's thunderbolt from the rebound was blocked on the line by a defender but Sigurdsson was on hand to stab home.
Clint Dempsey fired straight at Handanovic and Jan Vertonghen flashed a shot wide in the closing stages but Tottenham were unable to conjure up a winner.