The Premier League side went into the second leg holding a 2-1 advantage, and second-half goals from Olivier Giroud, Ross Barkley and Callum Hudson-Odoi sealed a comfortable win for under-pressure Maurizio Sarri.
Chelsea were under pressure to perform in front of their own supporters, and Malmo almost took full advantage as early as the third minute as Rasmus Bengtsson headed marginally over Willy Caballero's crossbar.
Chelsea grew into the game as it progressed but for all of their possession, their only shot on target during the opening half hour was a weak effort from Barkley and Malmo again threatened to take the lead with Markus Rosenberg dragging a low effort just wide.
Barkley was provided with another opportunity to get a shot away from distance just before the break but despite Giroud's run creating space for his teammate, Johan Dahlin made a comfortable save.
Both teams showed ambition after the restart but Chelsea effectively wrapped up the tie in the 55th minute, with Kante and Willian combining for Giroud to convert from close range for his sixth goal in this season's competition.
Malmo offered very little after going behind, and their task was made all the more tougher when Bengtsson was dismissed for a second yellow card when upending Emerson Palmieri on the edge of the area.
Barkley took responsibility for the free kick, and the playmaker was able to curl a 20-yard effort into the top corner with Dahlin not moving from the centre of his goal.
A three-goal advantage in the tie gave Sarri the chance to make his three substitutions in quick succession, with Kante, Barkley and Azpilicueta all being rested for the weekend.
Chelsea had been going through the motions but with six minutes remaining, Hudson-Odoi capped the perfect night for the Blues by drilling a low effort into the far corner of Dahlin's net from 12 yards out.
Ruben Loftus-Cheek could have added a fourth in added-on time only for Dahlin to make a timely block at the near post, but Chelsea and Sarri will be more than satisfied with a rare comfortable win ahead of the EFL Cup final with Manchester City and an important Premier League encounter with Tottenham Hotspur.
CHELSEA (4-3-3): Caballero; Azpilicueta (Ampadu 79'), Rudiger, Christensen, Palmieri; Kante (Jorginho 76'), Kovacic, Barkley (Loftus-Cheek 76'); Willian, Giroud, Hudson-Odoi
MALMO (4-4-2): Dahlin; Vindheim, Nielsen, Bengtsson, Safari; Traustason (Gall 72'), Christiansen (Lewicki 72'), Bachirou, Rieks; Antonsson, Rosenberg (Strandberg 62')