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.
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.
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.
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.
