The result means Sweden stay in second on 12 points, four points behind leaders Austria, who beat third-placed Russia 1-0 in Moscow. Montenegro lie fourth on five points.
The home side took the lead in the 38th minute after Ibrahimovic drifted out to feed Sebastian Larsson, who set Albin Ekdal free down the right and his pinpoint cross was firmly headed home by Marcus Berg.
Two minutes later it was Ibrahimovic's turn, collecting a throw-in on the left before cutting inside and thumping a shot from distance past Vukasin Poleksic, whose poorly-timed dive saw the ball squirm under his body.
Ibrahimovic netted his 56th goal for his country a minute before halftime, latching on to Larsson's long ball before coolly dispatching it past the helpless goalkeeper.
Dejan Damjanovic pulled a goal back for Montenegro midway through the second half, firing home a penalty after Stefan Mugosa was hacked down in the box, and they could have had a second moments later but for Andreas Isaksson, who got a hand to Fatos Beciraj's close-range effort.
Montenegro continued to chase the game, forcing the Swedes onto the backfoot for much of the second half, but the home rearguard held firm.
Ibrahimovic fought hard to complete his hat-trick and was forced to change shirts after his right sleeve was ripped off in one of many over-zealous duels with the Montenegrin backline, before being substituted in the final minute to rapturous applause.
(philip@eblana.se)
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