Spurs manager Jose Mourinho made three changes to the side that beat Ludogorets last Thursday, with Pierre-Emile Hojbjerg, Giovanni Lo Celso and Son Heung-Min all recalled.
The visitors were fortunate not to be a goal down as early as the sixth minute after Johannes Eggestein latched onto a rebound on the edge of the box before curling a low strike onto the far post.
Rene Renner had a wonderful opportunity to break the deadlock for LASK on the half-hour mark after going clear on goal but his shot was saved by goalkeeper Joe Hart in a one-on-one situation.
The Austrian side eventually broke the deadlock three minutes before the break from a counter-attack after Peter Michorl unleashed a rocket from range that sailed into the bottom corner.
Mourinho's charges were given a lifeline on the stroke of half-time after they were awarded a penalty for a handball by Andres Andrade, which allowed Gareth Bale to slot home the equaliser from 12 yards.
The Lilywhites were on the front foot after from the break and Son eventually gave his side the lead just before the hour-mark with a neat strike into the far corner after latching onto a through ball from Tanguy Ndombele.
After Bale missed a big chance, Spurs were punished in the last six minutes as Eggestein levelled matters for LASK with a powerful strike that Hart got a hand to but could not keep it out.
Dele Alli looked to to have secured the win for Spurs after converting a penalty soon after, but Mamoudou Karamoko equalised again for the Austrian side in stoppage time with a screamer from range to secure a share of the spoils.