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Sweden's first goal came after an Albin Ekdal cross from deep found Marcus Berg in plenty of space and the experienced forward was able to head the ball into the net.
Two minutes later, Ibrahimovic got his first goal of the night with a rasping shot across the goalmouth, before he got his second with a shot from the centre of the box just four minutes after the first.
Marko Simic, Zarko Tomasevic, and Vladimir Boljevic received yellow cards early on in the second half for Montenegro, before Stefan Mugosa was fouled in the penalty area and Damjanovic fired in the resulting spot kick to claw a goal back for his country.
The result leaves Sweden in second place in European Championship 2016 Qualifying Group F, while Montenegro remain in fourth.