Roberto Di Matteo’s Dons were looking for their seventh straight win but looked rusty after an 11-day break and didn’t have a clear-cut chance all match.
Early on, Alan Navarro inadvertently flicked the ball through for Scunthorpe’s Marcus Williams but his 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.
But not even Tore Andre Flo’s comeback to football could not inspire them and Scunthorpe grabbed their first with 13 minutes left.
Substitute Morris rifled in a superb 20-yard half volley home after a good knockdown by Hooper, then five minutes later fellow sub Thompson was left completely unmarked to tap in Williams’ cross at the back post.