The feisty Argentine flicked the ball to Kwado Asamoah in the penalty area and then ran on to the Ghanaian's back-heeled pass to slot the ball past Robin Olsen in the 59th minute.
He then secured the points by curling in a free kick from the edge of the area in the 90th minute of the Group A match.
Tevez's first goal bailed out Juventus who appeared to have run out of ideas as they battled a well-organised Malmo defence.
The visitors, who reached the 1979 European Cup final but had never qualified for the Champions League group stage, had the best first-half chance when Magnus Eriksson's close-range effort at the far post was stopped by keeper Gianluigi Buffon's feet.
Malmo, with an average age of just over 24, were anything but overawed as they kept Juve at bay for nearly an hour.
The hosts best chance came when Paul Pogba slipped a cunning pass through to Stephan Lichtsteiner but the Swiss defender failed to find Asamoah, who would have been left with a tap-in.
Lichtsteiner squandered another chance following an almost replica move early in the second half when his pass was cut out by Erik Johansson.
Olsen made a brilliant double stop to defy Fernando Llorente in the 84th minute, first parrying a header and then managed to scoop away the Spaniard's backheeled effort from the rebound.
(Reporting by Brian Homewood; Editing by Ken Ferris)
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