The Dons had all the chances in the first half but Luke Moore wasted the best of them when he failed to beat Alan Marriott.
However, Mansfield grew into the game after the break and only a succession of superb stops from Worner prevented them claiming a first league win since September.
Dons manager Neal Ardley was only able to name five substitutes due to injuries and suspensions but his side threatened first when Callum Kennedy fired over a 30-yard free-kick.
And it was the hosts who should have taken the lead three minutes before the interval when Stags keeper Marriott denied Moore in a one-on-one situation.
Ardley's men continued to press in the second half and Michael Smith headed over the crossbar before Worner produced a fine low save from Matt Rhead's header.
Worner was forced into another superb stop with eight minutes to go as he palmed away Sam Clucas' header.
There was still time left for the 24-year-old to make another telling save when Ross Dyer almost got on the end of a long free-kick.