The Grecians completely controlled the first half and had several chances to go in front. Jamie Cureton and Liam Sercombe both went close, while John O'Flynn was denied a clear penalty after being flattened by a combination of Will Antwi and Yado Mambo.
The opening goal eventually came after 32 minutes when Alan Gow played in Cureton with a brilliant reverse pass, he let the ball come across him before smashing a low shot into the far corner.
Wimbledon's only threat came on the stroke of half-time but Curtis Osano's shot deflected over the crossbar.
The Dons were far more impressive after the break and enjoyed a great spell of dominance. However, they did not create enough with their possession and O'Flynn added a second for Exeter after 71 minutes when he slotted into an empty net after good work by Craig Woodman and Scot Bennett.
Wimbledon never gave up but they lacked quality in the final third as City held on for three much-needed points.