That sparked a concerted period of pressure from the visitors that culminated with Morison and Bale swapping passes to send the Spurs wideman charging into the area.
Bale cut the ball across the face of the Montenegro goal but - with target man Morison involved in the build-up - no other Wales player had gambled on a run into the six-yard box.
Stung into action by that escape, Montenegro upped the tempo and Wales were soon hanging on grimly.
A speculative long strike by Branko Boskovic sailed wide, before a one-two saw Vukcevic break down the right and cut back inside to curl just wide of the far post.
Within a minute home skipper Vucinic glanced a header just wide of that same upright with Hennessey helpless, although the keeper did well to palm away a Boskovic shot as the DC United midfielder worked space on the edge of the area.
Wales failed to heed those warning signs and on 30 minutes fell behind as Vucinic scored a fine solo goal.
The Roma man went past James Collins with embarrassing ease and bore down on goal, placing his left-foot shot in off Hennessey's right-hand post as the Wolves stopper was caught anticipating a ball across him.
Montenegro goal scorer Mirko Vucinic (right) shares a moment with rival captain Craig Bellamy
Wales tried to respond but Morison had a penalty appeal turned down for a push and then Boskovic just managed to divert Bale's cross from the path of Bellamy, who had to check back and then sliced wide.
Vucinic almost grabbed a second on the stroke of half-time but Collins got in the way of his shot to deflect it wide.
Montenegro eased back into their stride after the break and a clumsy foul by Sam Ricketts gave Vukcevic the chance to fire a free-kick just over the bar.
A fine spin from Morison drew a clumsy challenge by Miodrag Dzudovic and gave Wales their own free-kick in shooting distance, although Bale was unable to curl his left-foot shot inside Mladen Bozovic's right post.
It was still Montenegro who had the clearer opportunities, though, and only a sliding block by Williams diverted Djalovic's goal-bound shot.
The defending from the resulting corner should have gifted Montenegro a second goal, but no home player was able to stick out a leg as Hennessey and his defence allowed the ball to bounce through the six-yard box.
Morison nearly fashioned an equaliser as the Millwall man nodded down a corner for Williams, only for Bozovic to throw himself bravely at the Swansea player's feet.
Earnshaw came off the bench in place of Dave Edwards as Wales manager Toshack opted for a second striker.
But moments later Collins had to be replaced by Craig Morgan after the Aston Villa defender took an elbow to the face from Dzudovic, although the Spartak Nalchik player - already booked - escaped any punishment.
Morison continued to offer Wales an aerial threat and again connected with a corner but his looped header was straight at Bozovic.
With the game into the final 10 minutes Bellamy had two chances in quick succession to grab an equaliser, first seeing his shot turned round the near post after being released by Bale's ball over the top and the skipper then headed weakly at the keeper from the corner.
Church came on for the hard-working Morison and so nearly grabbed an equaliser, first slamming a header off the crossbar and then being caught fractionally off-side as he slid home when Bozovic could not hold an Earnshaw shot.
Montenegro should have made absolutely sure deep in injury time as they caught Wales on the break, but Hennessey made some amends for a nervy performance with an outstanding one-on-one save to deny Vukcevic.
Montenegro: Mladen Bozovic, Savo Pavicevic, Marko Basa, Milan Jovanovic, Simon Vukcevic, Mirko Vucinic (Fatos Beciraj 87), Radomir Djalovic (Mitar Novakovic 83), Branko Boskovic (Vladimir Bozovic 73), Milorad Pekovic, Elsad Zverotic, Miodrag Dzudovic.
Wales: Wayne Hennessey, Sam Ricketts, Ashley Williams, James Collins (Craig Morgan 75), Chris Gunter, David Edwards (Robert Earnshaw 68), David Vaughan, Craig Bellamy, Steve Morison (Simon Church 78), Joe Ledley, Gareth Bale.
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