Armed with a healthy lead after an impressive first-leg triumph in Sweden, Lars Friis’ side looked full of confidence in the early stages.
The hosts’ positive start should have been rewarded with a breakthrough in the 19th minute when Nils Zatterstrom was adjudged to have fouled Asger Sorensen in the box, but Veljko Birmancevic fired the resulting penalty wastefully over the bar.
Grateful for that reprieve, Malmo were awarded a penalty of their own just eight minutes later. Anders Christiansen assumed the responsibility from the spot after being tripped in the area by Martin Vitik, however, like Birmancevic moments before, the Malmo midfielder fluffed his lines, with Peter Vindahl Jensen diving to his right to keep the scores level.
Sparta soon regained control of the contest before half-time and came close to extending their aggregate lead when Lukas Haraslin and Victor Olatunji spurned a couple of close-range chances.
Having picked up just two wins inside 90 minutes from their last eight matches, the visitors knew a fast start was needed in the second half to stand any chance of an unlikely turnaround.
However, clear-cut opportunities came at a premium for both sides, with Sparta happy enough to preserve their advantage going into the final 20 minutes.
Kaan Kairinen threatened an opener for the hosts when his free-kick cannoned off the bar, and the breakthrough finally arrived shortly afterward in the 80th minute, with Haraslin converting from the spot after a clumsy challenge from Busanello.
That killed off any hopes of a Malmo comeback, and Sparta rubbed salt in the wound by adding a quickfire second via substitute Albion Rrahmani, who tapped home from Haraslin’s inviting delivery to put the seal on a historic night for Friis’ men.
Flashscore Man of the Match: Lukas Haraslin (Sparta Prague)
Check out the match stats here.
Young Boys and Salzburg join Prauge in Champions League
BSC Young Boys qualified for the UEFA Champions League for the second season running after a 1-0 victory on the night was enough for the Swiss visitors to run out 4-2 winners on aggregate and knock Galatasaray out of the competition.
As for Salzburg, they qualified for the UEFA Champions League proper for a sixth successive season, as a 1-1 draw on the night helped them to a 3-1 aggregate victory over Dynamo Kyiv.