Celtic took a huge step towards the Champions League as two stunning Camilo Duran strikes helped carve out a commanding first-leg play-off lead against LASK.
The Colombian struck fabulous efforts either side of half-time after a wonderful finish from Bejamin Nygren set the Scottish champions on their way.
LASK did threaten throughout and had the ball in the Celtic net twice in the first-half, but both goals were ruled out for offside.
The sides meet again in the second leg next Tuesday (20:00 BST) in Linz.
On a typically raucous European night at Celtic Park, LASK stunned the home crowd within 30 seconds when they had the ball in the net.
Cameron Carter-Vickers was caught out by a ball over the top and Moses Usor raced through and dispatched a ruthless finish into the top corner, but the flag went up.
Celtic looked nervy, LASK looked confident, and moments later Carter-Vickers was outpaced by Samuel Adeniran and the American striker should have done better than to drag his strike wide of the target.
The Austrian champions were content to cede possession, sit deep and counter. Their tactics looked spot-on until they were undone by a moment of brilliance.
The ball dropped to Nygren at the edge of the box and the prolific Swede curled a wonderful strike into the top corner to change the dynamic of the match.
LASK thought they had an equaliser when George Bello's pinpoint cross found Adeniran completely unmarked eight yards out and he bulleted a header past Viljami Sinisalo, but again the offside flag was up.
Both sides looked threatening and another magnificent goal doubled Celtic's lead.
A dangerous cross aimed for Kasper Hogh was headed away, but only as far as Duran at the edge of the box and he unleashed an unstoppable rocket of a volley past Lukas Jungwirth.
Celtic upped the tempo after the break with Callum McGregor's deflected strike crashing back off a post and, while LASK caused further moments of panic at the back, the third goal arrived courtesy of Duran.
A smart one-two with Nygren opened up a little space in the box and the Colombian slotted a lovely finish high into the net to give his side some breathing space in the tie and further endear himself to the Celtic fans following his summer arrival.
LASK hunted the goal that would lessen the scale of their task in Linz next week, but Sinisalo dealt with everything that came his way as Celtic preserved a commanding lead to take to Austria.