The victory came thanks to a pair of goals from 32-year-old Markus Rosenberg.
"I don't really know what was going through my head afterwards," he told the Aftonbladet newspaper. "It was just happiness."
The Swede scored in the 42nd and 82nd minutes, taking Malmö past the Greek side and landing the team in equal first position in group A with Olympiacos, Juventus, and Atlético Madrid.
Malmö progressed to the group stages following Uefa's decision to tweak rules on participation for national champions in affiliated countries.
It was the first group stage match in Sweden since in November, 2000, when Helsingborg drew 1-1 with Paris Saint-Germain.
Malmö will face Atlético Madrid in Spain on October 22nd.