The visitors were in front less than 10 minutes in as Zlatan Ibrahimovic collected the ball inside the six-yard box and found the top corner with a thumping strike.
Montenegro's best chance for an equaliser in the opening 45 fell to Jovetic shortly before half time, but the forward's header was saved by visiting goalkeeper Andreas Isaksson, whose awareness preserved Sweden's lead at the break.
Jovetic came close again shortly after the hour mark when he gave his marker the slip in the final third and went for goal, with his shot taking a deflection before bobbling a few yards wide.
Montenegro continued to press for an equaliser, and they got one from the penalty spot nine minutes from time when Oscar Wendt was adjudged to have fouled Vladimir Jovovic in the box, allowing Jovetic to smash home from 12 yards and make up for his earlier misses.
The result moves Sweden into second place in Group G, while Montenegro go level on points with third-placed Russia.