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The Swedish outfit threatened early on at the Vicente Calderon when an Isaac Thelin effort was blocked after just 40 seconds on the clock.
Just a few minutes later, Markus Halsti came close to opening the scoring from a corner, but his header flew just over the crossbar.
It didn't take long for the Spanish champions to regain a foothold in the game, however, with Arda Turan's header on the quarter-hour mark floating just wide, while Juanfran and Saul Niguez also caused Malmo problems minutes later.
As the game went on, chances became more and more frequent, as both sides pushed forward and attacked at every opportunity, but they were unable to break the deadlock come half time.