With Atletico Madrid winning against Olympiacos, the Italian champions moved into second place with a three-point cushion, as Fernando Llorente and Carlos Tevez delivered the decisive goals.
Malmo goalkeeper Robin Olsen ensured the two sides went into the break level with three important saves to deny Arturo Vidal and Claudio Marchisio, twice.
However, Malmo's resistance was finally broken early in the second half as Llorente netted his first goal of this season's competition with a composed finish.
Chances continued to arrive for the visitors and after Marchisio and Llorente had wasted good opportunities, Tevez secured the win with two minutes to play, before defender Erik Johansson was sent off for the hosts.
Victory means a point against Atletico in their final group match will see Juve through, no matter what Olympiacos do, while Malmo's adventure in the competition is over.
Massimiliano Allegri made two changes from Juve's Champions League win over Olympiacos on matchday four, with Simone Padoin - who was sent off against Lazio in Serie A on Saturday - and Llorente coming into the side.
After a fast start from the hosts, who were unchanged from their last European outing against Atletico, the game's first effort on goal did not arrive until the 16th minute, as Stephan Lichtsteiner raced down the right wing unopposed.
Malmo failed to deal with the full-back's cross, allowing Vidal a free shot from the edge of the penalty area that Olsen had to be alert to parry.
Juve continued to push for the opening goal and Marchisio had two chances before the break, only to be denied by Olsen on both occasions.
His first effort after 28 minutes came following a chipped pass from Andrea Pirlo, but the midfielder was unable to divert the ball past Olsen, and seven minutes later the goalkeeper made a superb reaction save to deny the 28-year-old again.
Malmo's only effort of the first half came in the closing minutes, as Emil Forsberg jinked past the Juve defence only to see his low effort beat Gianluigi Buffon but end up in the side netting.
Marchisio's personal battle with Olsen continued in the opening minute of the second half, but once again the 24-year-old got down well to keep the Italy international at bay.
Two minutes later the goal came, though, as Marchisio turned provider with a defence-splitting pass for Llorente, the Spanish forward rounding Olsen to fire home from six yards.
Having been a mere spectator for much of the second half, Buffon was finally called into action after 64 minutes when Enoch Adu found space on the edge of the penalty area, but the Juve goalkeeper had no trouble gathering a tame effort.
Llorente should have doubled his tally with 20 minutes to play as he rose to meet a Padoin cross from the left, but he headed straight at Olsen.
Juve doubled their advantage with two minutes left as Paul Pogba broke free in the Malmo half before playing in Tevez, the Argentine striker scuffing his shot past Olsen and into the goal.
To add to Malmo's frustration, they were reduced to 10 men following the goal as Johansson was sent off for a second-bookable offence in the build-up.
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