Malmo 1 Chelsea 2
Olivier Giroud scored his fifth goal in four Europa League games as Chelsea won the first leg of their last-32 tie.
Ross Barkley put them ahead after half an hour and Giroud struck 13 minutes into the second half.
Chelsea were well in control in Sweden but a mistake by Andreas Christensen led to a late goal for Malmo.
Maurizio Sarri’s side went in front when Rasmus Bengtsson failed to clear Pedro’s cross and Barkley helped himself to his first European goal.
And, with the Blues under second-half pressure, Giroud struck on the counter-attack with a classy second.
Willian was found by Barkley and delivered the ball from the left to Giroud, who nonchalantly flicked it into the net.
Chelsea looked comfortable at that stage but the defensive shortcomings which have blighted their season became evident again.
Markus Rosenberg pounced on a poor touch by Christensen and delivered a superb ball towards Anders Christiansen, who got in front of Mateo Kovacic to score.
Nevertheless, Chelsea are very much on course for the last 16 after their first win – and goals – away from home since the turn of the year.
Chelsea: Kepa, Azpilicueta, Christensen, Luiz, Emerson, Jorginho (Kante 74), Kovacic, Barkley, Willian (Hazard 71), Giroud, Pedro (Hudson-Odoi 84).
Subs not used: Caballero, Rudiger, Zappacosta, Higuain.