David Healy kept Norwich City within touching distance of the First Division play-offs with his strike in the 40th minute.
The Northern Ireland international capitalised on some good work by Zema Abbey to grab a deserved lead for the Canaries.
Abbey thought he had doubled the Canaries' advantage just after the hour mark
but his close-range strike was ruled offside.
That let-off inspired Wimbledon who battled back gamely but they could not find a way past Norwich goalkeeper Robert Green.
The game at Carrow Road opened frenetically and the Dons were grateful to keeper Kelvin Davis who somehow got a hand to Paul McVeigh's dangerous 20-yard effort.
But it was not long before Norwich beat Davis when Abbey did well to flick a hopeful ball into the box into Healy's path.
The striker fired a fierce left-footed drive from 18 yards
into the back of the net.
The interval failed to halt Norwich's momentum as the Canaries went in pursuit
of a second goal.
And it nearly arrived when Abbey prodded the ball home after McVeigh struck the post, only for him to be judged offside.
That decision nearly cost the home side as a swift Wimbledon counter-attack
put Adam Nowland one-on-one with Green.
But the Canaries keeper made a stunning double save to deny Nowland of his second goal of the season and virtually wipe out Wimbledon's chances of finishing in the top six.
Norwich: Green, Nedergaard, Mackay, Kenton, Drury, Rivers,
Russell, Holt, McVeigh, Healy, Abbey.
Subs: Crichton, Roberts, Nielsen, Easton, Bromby.
Wimbledon: Davis, Volz, Nowland, Chorley, Hawkins, Tapp, Morgan, Reo-Coker, Darlington, Shipperley, Connolly.
Subs: Gore, Holloway, Agyemang, Gray, Gier.
Referee: M Fletcher (Worcestershire).