Celtic Park was rocking at kick off but they were stunned into silence after less than 30 seconds when Moses Usor rifled home a volley from a narrow angle but the offside flag came to Celtic’s rescue.
There was another scare just two minutes later, when Samuel Adeniran outpaced his countryman Cameron Carter-Vickers but the American forward slid wide.
Having been let off the hook early on, Celtic gained a foothold and Benjamin Nygren picked out Camilo Durán in the box and he forced a good stop from Lukas Jungwirth after 10 minutes.
The game settled after this until the 26th minute, when Kieran Tierney broke down the left and delivered a dangerous cross that was only half cleared by Sascha Horvath into the path of Nygren, and the Swedish midfielder unleashed a controlled first-time strike into the top corner.
That had the home fans in fine voice again but the Austrian champions struck back quickly as Adeniran headed home George Bello’s cross but, once again, the linesman ruled it out.
Martin O’Neill’s men took full advantage of this once more seven minutes before the break, and it was Tierney again causing trouble down the left with his cross headed out to Durán this time, and the Colombian smashed a stunning volley into the top corner.
The Scottish champions were clearly finding their range from distance and, just before the hour, captain Callum McGregor hit a shot from outside the box that took a couple of ricochets, the last of which came off his teammate Kasper Høgh and on to the post.
Dietmar Kühbauer’s men then came into the match a bit more, but they were made to pay for their wastefulness, and it was Nygren and Durán who combined again to devastating effect.
The latter cut in off the right and played a delicious one-two with the former before curling one into the top corner that Jungwirth got a hand to but couldn’t keep out.
LASK had scored 16 goals in their first four competitive games this season, and even a consolation would have been crucial for their hopes of overturning the tie on home soil next week.
However, despite four of their last six home competitive games finishing 3-1, Celtic locked the door and kept Die Schwarz-Weissen at bay.
The task is by no means complete as the tie shifts to the Raiffeisen Arena in Linz next week, but Celtic are very much in the driving seat.
Flashscore Man of the Match: Benjamin Nygren (Celtic)