The win at Swedbank Stadion provides a bit a relief for embattled boss Maurizio Sarri following Sunday's 6-0 drubbing to Manchester City and ahead of a FA Cup clash with Manchester United.
The Blues took the lead in the 30th minute when Malmo defender Lasse Nielsen had trouble clearing the ball, allowing Barkley to jump in and get the score.
Giroud doubled it for Chelsea's in the 58th minute after flicking in Willian's cross in front of the net, built up from Barkley's counter-attack.
Malmo pulled one back in the 80th minute when Anders Christiansen chased down Markus Rosenberg and comfortably put it past Kepa Arrizabalaga.
The second leg is set for Feb. 21 at Stamford Bridge.