Alli scored a stunning bicycle kick in the first half before setting up Carlos Vinicius and substitute Gareth Bale in the second as Jose Mourinho's side eased to an 8-1 aggregate victory.
Spurs' third win in nine games in all competitions, capped by a second from Vinicius, was a routine but welcome one, particularly for Mourinho, who was able to rest stars including Harry Kane and Son Heung-min as he looks to put together a string of results and ease some of the speculation over his future.
Spurs have made something of a habit of starting well this season – in fact, no Premier League team can match their tally of 11 goals in the first 10 minutes of matches in all competitions – but they have rarely broken the deadlock with such a flourish.
Alli played the ball out wide to Matt Doherty, brought down his cross and sent a sublime overhead kick out of the reach of goalkeeper Manuel Kuttin and into the left-hand corner.
Vinicius should have made it 2-0 before the break after rounding Kuttin, but the covering Gustav Henriksson did superbly to clear the striker's effort off the line.
He made no mistake early in the second half, though nodding in Alli's deep cross shortly after Eric Dier had been fortunate to escape punishment for taking out Cheikhou Dieng when the forward was through on Joe Hart's goal.
Spurs got their 100th Europa League goal 17 minutes from time, Bale sweeping an emphatic finish high into the net from Alli's pass after Harry Winks had pressed Wolfsberger into giving the ball away in their own half.
Mourinho handed debuts to Marcel Lavinier and Nile John, while 16-year-old Dane Scarlett was given more first-team experience, the latter setting up Vinicius to blast home his second and Spurs' fourth with seven minutes left.