Jim Bentley's in-form side took the lead that sent them to the top of the table for a short period but a goal from Wimbledon striker Michael Smith early in the second half earned the Dons a share of the spoils.
Morecambe took the lead in the seventh minute thanks to a stunning strike from Kevin Ellison. Stewart Drummond played the ball down the right-hand side, Ellison cut inside on to his left foot and curled a fierce effort past Ross Warner from a tight angle.
But Smith hit back with a close-range header six minutes after the break. On-loan Burnley winger George Porter sent over a deep cross and Smith beat Barry Roche to the high ball for his sixth goal of the season.
The rest of the game saw few chances. Porter's effort flew wide and Smith tried his luck with an overhead kick while Morecambe failed to test Worner in a poor second half show.