The visitors only had one shot in the first half, but should have scored with it after 11 minutes. Amady Camara cut inside well, but unleashed his shot wide of the near post, perhaps showing why he has gone nine games without scoring.
In contrast, Mateo Retegui has been in fine goalscoring form for Atalanta this season, and he punished the missed chance moments later by tapping in his third goal in as many matches from Davide Zappacosta’s cutback.
The hosts dominated from there until HT, and Zappacosta could have netted himself, curling just a whisker over the top corner of the goal.
Retegui had an opportunity to score his brace too, sending a diving header over at the back post after connecting with Lazar Samardžić’s whipped corner.
And Atalanta continued their dominance into the second half, as Kjell Scherpen was called into action early when Sead Kolašinac flashed a shot towards the far corner, but the goalkeeper tipped it wide.
They did have the ball in the net shortly after, but Charles De Ketelaere’s goal was disallowed for an offside in the build-up, as substitute Ademola Lookman was offside when he fed the Belgian.
Another substitute, Juan Cuadrado, then hit the post in what was a nervy opening few minutes for Sturm Graz, before Lookman fired straight at Scherpen from close range.
Scherpen denied Lookman again shortly after before the hosts finally doubled their lead, as Mario Pašalić touched home Cuadrado’s cross.
The net simply kept bulging, and De Ketelaere did not have to wait long to get on the scoresheet, as he poked home his 11th of the campaign following a corner routine. Cuadrado then put in another brilliant ball for Lookman, but the Nigerian could only fire over.
The hosts were denied a fourth by the offside flag again as Zappacosta struck late on, but Lookman made sure of the scoreline with a headed goal just before stoppage time.
That was not the end of the scoring though, as Marco Brescianini slotted past Scherpen after the ball fell kindly to him in the box. Atalanta, at least temporarily, rise to third place in the UCL league phase table, while Sturm Graz are knocked out of European competition.