Montenegro gave Wales a scare in the first minute at the Cardiff City Stadium when Stevan Jovetic broke through, only to screw his shot well wide.
Welsh nerves continued to jangle as Blake let a long ball bounce over his head and only Wayne Hennessey's swift advance from his line prevented Mirko Vucinic sneaking in.
The Montenegro captain was finding space at will and followed up with a speculative shot that he scuffed wide, after Wales were slow in closing down the Juventus striker.
Wales at last threatened as Bale found space down the right and arced in a high ball for Joe Ledley in the Montenegro area.
The Celtic midfielder appeared to be bowled over by Milorad Pekovic but Italian referee Luca Banti waved play on.
Craig Bellamy was following up but he could only hit the difficult volley into the ground, taking the sting out of it before it reached goalkeeper Mladen Bozovic.
But with their next attack Morison gave Wales the lead with his first international goal, stabbing home from close range after Bozovic failed to hold Vaughan's cross from the left.
Montenegro's early composure was shaken by that set-back and a visibly buoyed Wales nearly added a second goal when Bale broke past two defenders and fired a long-range shot that Bozovic tipped over.
After a booking for Vaughan, which rules him out of Tuesday's game with England, Radomir Dalovic had a great chance to equalise when Montenegro opened Wales up down the right but shot wide.
Wales were now driving forward at will and Ashley Williams had a header cleared off the line from a corner.
Wales' Euro 2012 fixtures
TUESDAY, 6 SEPTEMBER
v England (Wembley)
FRIDAY, 7 OCTOBER
v Switzerland (Swansea)
TUESDAY, 11 OCTOBER
v Bulgaria (Sofia)
As the half closed Bale and Ledley both went close with good efforts, but Bellamy picked up a yellow card for an innocuous challenge that also rules the new Liverpool man out of the trip to Wembley.
Wales began the second half as they ended the first, closing down Montenegro quickly and the pressure told as Bale surged into the box and pulled the ball back for skipper Ramsey, arriving on cue, to double their lead.
Bale worked Bozovic again as he was left unmarked in the Montenegro area but could not get enough power on his header from a looping cross.
The Tottenham wing was causing havoc down the right and when he broke past the bemused Sasa Balic once again, Bellamy was millimetres from connecting with his cross as the Liverpool striker hurled himself at the ball.
Wales boss Speed withdrew Ramsey on 64 minutes and sent on the more defensive Andrew Crofts in his place.
Montenegro had hardly threatened in the second period but served notice they were still potent as Nikola Vukcevic took a smart pass from Jovetic and cannoned a shot off Hennessey's shins.
But Jovetic then pulled a goal back as he cut inside Chris Gunter to hammer home right-footed and give the visitors hope.
With five minutes remaining Hennessey was down well to block another Vukcevic shot, while Gunter was smartly in to punt away the dangerous loose ball.
In a frantic ending Blake and Crofts pulled off brilliant tackles and Hennessey a string of saves to keep Montenegro at bay and earn Speed his first qualifying success as Wales manager.
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