Gareth Bale made his first start for Spurs since his well-documented return, as Joe Hart started in goal with Matthew Doherty, Lucas Moura and Erik Lamela the other key inclusions.
The Austrian side's game-plan was thrown into jeopardy after three minutes when James Holland went down injured before being replaced by Lukas Grgic.
Moura gave Spurs the lead on 18 minutes after combining with his countryman Carlos Vinicius before applying a composed finish inside the six-yard area.
Spurs made it two goals nine minutes later when a stroke of good fortune saw Andres Andrade struck Bale's low cross from the right past his own goalkeeper Alexander Schlager.
A second injury enforced change for LASK had Rene Renner hauled off on 39 minutes after a collision with Pierre-Emile Hojbjerg and replaced by Petar Filipovic.
Hart was tested for the first time a minute to halftime when he answered Husein Balic's left-footed drive from the area with a stupendous palm.
Spurs' first-half dominance carried over to the second half with Lamela seeing a low shot inside the area blocked, while Schlager beat Bale to a ball over the top.
Filipovic was unfortunate not to halve the deficit towards the latter stages from a glancing header at the near post following a corner-kick, as the attempt flew across Hart's goal.
Spurs regained control and found a third goal in the last six minutes when a cutback on the edge of the area from Vinicius released Heung Min-Son who found the bottom-corner to round off the win.
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