Juventus struggled at times before Tevez broke the deadlock in the 59th, following good interplay with Kwadwo Asamoah.
It was the Argentina forward's first goal in Europe's elite club competition in more than five years ago.
Tevez then sealed the result in stoppage time with a well-placed free kick that sailed into the top corner.
The Bianconeri dominated possession against the Swedish minnows, but failed to create many clear cut opportunities, and it was Malmo which almost took the lead in the first half.
In the other group match, Olympiakos surprisingly beat last year's runner-up Atletico Madrid, 3-2.