The Blues headed into the game licking their wounds after the heavy 6-0 defeat at the hands of Manchester City at The Etihad on Sunday in the Premier League.
That loss heaped the pressure on Chelsea FC boss Maurizio Sarri as it dropped his side down into sixth place in the Premier League table.
However, goals from Barkley and Olivier Giroud helped Chelsea FC to claim a 2-1 win over Malmo and take a step closer towards reaching the last 16 of the Europa League.
Manchester United will now turn their attentions towards their crunch FA Cup fifth-round clash against Manchester United at Stamford Bridge on Monday night.
And Barkley has talked up the importance of the Blues continuing their strong form after Thursday night’s win.
Speaking in an interview with Chelsea FC’s website, Barkley said: “It was important for us to get the result from the weekend behind us and start with a positive today and a win.
“It was vital for us to win today and hopefully it continues. To come away from home and win was the target today and we’re looking forward to the second leg.”
Barkley has scored four goals and made five assists in all competitions for Chelsea FC so far this season.
Meanwhile, Manchester United will head into Monday’s game on the back of their disappointing 2-0 loss to Paris Saint-Germain in the last 16 of the Champions League on Tuesday night.
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