The home side turned in their best performance under Gary Speed and were unrecognisable from the side that lost so miserably to Australia last month.
Morison tapped in the opener in the 29th minute when Montenegro keeper Mladen Bozovic failed to hold a David Vaughan cross, before Ramsey slotted home after the break thanks to great wing play by the outstanding Gareth Bale.
Despite seeing his side pick up a first win in a competitive fixture since October 2009, there was bad news for Speed in the form of the bookings picked up by Vaughan and Craig Bellamy, who will miss Tuesday's trip to face England at Wembley.
Montenegro pulled a goal back through Stevan Jovetic but they could not find a leveller and they now trail England by three points at the top of Group G, after Fabio Capello's side won 3-0 in Bulgaria, with two games to play.
Speed, who brought Darcy Blake and Morison into his XI, had warned his side they could not repeat the slow starts that had proved so costly in defeat to England and Australia, but they were again sluggish out of the blocks.
The Montenegro triangle of Jovetic, Simon Vukcevic and Mirko Vucinic was causing the Welsh midfield all sorts of problems with their precise passing and movement, finding space with a minimum of fuss.
They served early notice of the threat they posed with Jovetic firing wide with a left-footed shot from the edge of the box.
Vukcevic then linked superbly with skipper Vucinic, with the striker dragging an effort from distance across goal as the visitors assured start continued.
But Wales slowly grew into the game, with Bale, playing predominantly on the right, and Bellamy proving particularly lively down the flanks, and it was they who took the lead in the 29th minute.
A composed build-up ended with Vaughan surging into the box and, when keeper Bozovic failed to hold on to his cross, the Norwich striker tapped in only Wales' second goal of the campaign.
Wales were on top for the remainder of the half and were unlucky not to double their lead as Joe Ledley narrowly failed to get on the end of a Bellamy cutback and Bale went close from distance, before Elsad Zverotic cleared an Ashley Williams header off the line after more uncertain work by keeper Bozovic.
But Wales were then dealt a double blow as Vaughan and Bellamy picked up bookings, the latter harshly awarded for pulling back, that will see them miss the trip to Wembley.
The hosts shook that off to deservedly double their lead just five minutes into the second half thanks to more superb play from Bale.
Williams' long ball forward found the Tottenham man, who turned his marker inside and out before teeing up Ramsey for a simple finish into the left-hand corner.
Ramsey was withdrawn shortly after with Andrew Crofts taking his place, and Wales began to lose control of a game they had been dominating.
And Jovetic then pulled a goal back as he cut inside Chris Gunter to hammer home and give the visitors hope.
The visitors could have been level moments later but substitute Dejan Damjanovic blazed high and wide from close range.
Bale curled wide at the other end as the game became increasingly stretched with Montenegro desperately seeking an equaliser.
Wayne Hennessey then saved from Vukcevic after an incisive break but Wales just about held out to give Speed his first win in a competitive fixture.