Roma striker Vucinic, linked with both Manchester clubs earlier this year, struck after 30 minutes to hand the hosts a deserved Group G victory against a ragged Welsh side.
Wales' best moments all came in the closing minutes as Simon Church headed against the bar and then had a goal disallowed.
Prior to that Montenegro had carved out all the best openings at the Gradski Stadium and impressive captain Vucinic could easily have had a hat-trick.
Wales were largely frustrated at the start of a campaign they were beginning with much optimism, with the threatening Gareth Bale marked out for some particularly close treatment. Yet Montenegro's determination to stop the likes of Bale and Craig Bellamy could not detract from a display full of attacking vigour and intent which will serve as a warning to England next month.
And Montenegro, who are coached by former Croatia boss Zlatko Kranjcar, the father of Bale's Tottenham team-mate Niko, were without another dangerous striker in Stevan Jovetic.
Both teams were clearly intent on attacking and the game got off to a lively start.
Bale and Bellamy were both playing in advanced roles on the left and right respectively, forming a three-man attack with Millwall striker Steve Morison, who was winning his second cap.
Montenegro looked sharp and had the first effort on goal when their direct approach created a chance for Elsad Zverotic but his effort flew over.
Joe Ledley had a similarly misdirected shot for Wales as the visitors launched a quick counter-attack.
Wales survived a scare when Sam Ricketts slipped allowing Simon Vukcevic to get in a fierce shot.
Wayne Hennessey palmed the ball behind and then leapt to punch away the resulting corner.
Wales responded with Bellamy breaking free down the right and firing in a cross but Ledley failed to trouble Mladen Bozovic with his header.
Intricate play then allowed Bale to weave his way into the box with a tricky run down on the right but Montenegro scrambled his cross clear.
Montenegro began to up the tempo as Radomir Djalovic shot narrowly wide from 30 yards and a cross-shot from Vukcevic flew untouched across the face of goal.
Vucinic then spurned a glorious chance when he headed wide from an unmarked position in front after being picked out by Savo Pavicevic following a rampaging run.
Hennessey then needed to be alert to beat out a shot from Boskovic after neat interplay with Vucinic and Djalovic on the edge of the area.
There was an inevitability about Montenegro's goal on the half-hour as Roma striker Vucinic showed the quality that has made him one of the hottest properties in Serie A.
Vucinic beat James Collins with a quick turn of pace and then unleashed a powerful left-footed shot which rebounded off the near post and went into the net.
Wales tried to respond but Morison had a penalty appeal turned down for a push and Bellamy sliced a shot well wide.
Vucinic almost grabbed a second on the stroke of half-time but Collins just managed to get in the way of his shot.
Montenegro went close again four minutes into the second half when Vukcevic curled a free-kick narrowly over.
It began to look like a set-piece might offer Wales their best hope of getting back into the game but Bale shot wide from 25 yards when a foul on Morison gave them an opportunity.
Montenegro continued to hammer at the Wales defence and Djalovic had a good shot blocked, leading to the first of a succession of corners.
Wales survived a few moments of alarm in their own area and broke out as Bale, frustrated on the left after being given close attention by his markers, switched flanks.
He won a corner and then delivered a dangerous cross from which Ashley Williams forced anxious goalkeeper Bozovic to turn over his bar.
Bellamy tested Bozovic again seven minutes from time when he burst into the area on the right but his shot was turned away for a corner.
Cardiff's on-loan forward then should have done better when he headed straight at Bozovic from Bale's cross.
Wales at last began to create openings in the in the closing minutes but Church was twice denied in a frantic finish.
First he saw a header rebound off the bar after reaching a Bale cross then he was flagged offside when he stabbed home a rebound after a Robert Earnshaw shot was saved.
Vucinic should have claimed a second for Montenegro in injury time but Hennessey stood up well.