The result left Sweden second on six points from four games, one ahead of Montenegro and Russia and four behind leaders Austria who beat the Russians 1-0 earlier on Saturday to stay firmly in the driving seat.
The Swedes will feel hard done by after Scottish referee William Collum disallowed an added time goal by midfielder Albin Ekdal and awarded Montenegro a contentious free kick for what looked like off-the-ball tugging between two players.
Ibrahimovic, having recovered from a niggling heel injury which kept him out of Sweden鈥檚 last two qualifiers — a 1-1 draw with Russia and a 2-0 win over Lichtenstein — silenced a raucous home crowd with a fortuitous ninth-minute effort.
He headed a long ball towards the penalty box and, when a clearance by Zarko Tomasevic rebounded off Sweden midfielder Erkan Zengin back to him, Ibrahimovic side-footed a first-time shot past keeper Mladen Bozovic.
It was his 51st goal in 101 internationals and the towering striker missed several chances to add to his tally, hitting the post with a ferocious free kick in the second half after blasting high an easy chance midway through the first.
Manchester City striker Jovetic had a powerful header saved by Andreas Isaksson shortly after the Montenegrins fell behind but despatched the spot kick after Vladimir Jovovic was fouled by two defenders as he burst into the area from the right flank.
Montenegro centre back Marko Basa skied a shot over a gaping net from two metres in a frantic finish before the home fans twice let out a huge sigh of relief when Ekdal first returned the favour and then saw his rasping volley ruled out by Collum.
(Writing by Zoran Milosavljevic; Editing by Ken Ferris)