After not playing in 11 days the Dons looked very rusty in the first half and in the first 15 minutes gifted the visitors two great chances.
Firstly Alan Navarro inadvertently flicked the ball through for Marcus Williams, whose powerful left-foot shot was well parried by Willy Gueret.
Then Carl Regan's clumsy back header went straight to Gary Hooper who turned well in the box and hit a snap shot just past the post.
Dons just couldn't get any foothold in the game, were sloppy in possession and lacking ideas and creativity up front.
They then gifted Hooper another golden opportunity as on-loan West Ham defender Bondz N'Gala stupidly let the ball run behind him and the pacy Hooper picked his pocket and went round the Gueret, only for Regan to rescue the situation and clear.
Dons did eventually start to wake up as the half went on. Jason Puncheon faked to shoot before hitting a shot that required a smart save from Joe Murphy.
Then Ali Gerba's clever flick from Shaun Cummings' low cross forced a decent reaction save from Murphy.
Dons came out with a little more energy in the second half, but they still couldn't fashion a clear-cut chance. Puncheon had several long-range efforts that missed the target.
The Cowshed were after a penalty when Sam Baldock was outmuscled in the penalty area, but the referee got it spot on as he waived play on.
Then with 13 minutes left Morris hit the Dons with a superb strike. He got on the end of a knockdown and hit a fierce half-volley into the roof of the net from 20 yards.
Then five minutes later Thompson was left completely unmarked to tap in Williams' cross at the back post and seal a deserved win.