Norwich picked up a precious three points but made heavy weather of the second half keeping the large Canaries following on the edge of their seats until the final whistle.
The home side started in determined fashion and did most of the attacking throughout the first half.
The Dons were forced to make an early substitution, Jermaine Darlington limping off to be replaced by Rob Gier after just 15 minutes.
Kelvin Davis then excelled himself with a fine save to keep out a curling shot from Paul McVeigh.
The only goal of the game came five minutes before the break when Zema Abbey headed on a long clearance into the path of David Healy and his left foot shot found its way inside the keeper's left-hand upright.
On the hour Healy tested Davis with a long-range effort but the keeper made a safe catch under his crossbar.
Abbey netted in the 64th minute when McVeigh's shot rebounded off a post but an offside flag cut short the celebrations.
Darren Holloway replaced Lionel Morgan after 65 minutes before Adam Nowland brought a fine reflex save from Robert Green.
Alex Tapp was booked for a foul on Steen Nedergaard and Dons skipper Neil Shipperley was booked for something he said.
Tapp was replaced by Patrick Agyemang and Moritz Volz was booked for a late tackle on Adam Drury.
As the game went into three minutes of nail-biting stoppage time veteran striker Iwan Roberts replaced Abbey but most of the action in the last few moments was in the Norwich penalty area with Wimbledon forcing two of their three corners in an exciting final minute.