As Morecambe had midfielder Craig Stanley off the field nursing an injury the visitors took advantage of the space afforded to them by the ten men as Dyer hammered home a shot from the edge of the area after a quickly-taken free-kick.
It proved to be the decisive moment of a game which saw newly promoted Morecambe more than match their high-flying opponents.
Paul Ince's side played some neat possession football, but it was Morecambe who created the better chances. Unfortunately for them striker Michael Twiss had an off day and wasted the opportunities that came his way.
Twiss should have given the Shrimps the lead on eight minutes when Morecambe's star man Garry Thompson broke free down the right. His cross was only half cleared, but with an open goal in front of him, Twiss skewed the shot wide.
A minute later Twiss failed to connect with Thompson's neat cross before wasting a glorious opening just before the break. Matty Blinkhorn's flick on left Twiss with only Willy Gueret to beat, but his lob was too high and the ball sailed over the crossbar.
The second half saw few clear cut opportunities and it was Morecambe who always looked the more likely to score.
Carl Baker fizzed a left-foot shot inches wide and David Artell saw a header cleared off the line by Danny Swailes.
Thompson forced Gueret into a neat save low to his left before flashing another effort wide of the left-hand post.
The Dons always looked sharp on the break and Dyer should have done better than send a right-foot drive of the left-hand post with players over.
Jude Sterling thought he had made it 2-0 when he scored from close range after Lewis' save, but his 81st minute effort was ruled out for offside.
Morecambe pushed to the death but just could not break through a resolute and well marshalled Dons' defence, who claimed their fourth successive clean sheet.