Yeovil themselves badly needed maximum points after being sucked into the relegation dogfight. They had lost their last three games without scoring a goal, and were without a point since a draw at Milton Keynes a month ago.
They dominated play for long periods, but their attractive and purposeful approach work failed to have the desired result until the 71st minute when Chris Cohen, on loan from West Ham, slipped a pass to Kevin Gall and the recently recalled striker fired past Matt Baker.
Gall had earlier had an effort disallowed for offside, but when he scored the Glovers seemed to be heading for a deserved victory.
They had pounded away in the early stages of the second half, forcing half a dozen corners and putting pressure on the Dons defence.
But although the visitors' attacks were infrequent, they should have taken the lead in the 57th minute.
With most of the Yeovil team in the Dons half, goalkeeper Baker booted a long clearance upfield and Izale McLeod was left with only home goalkeeper Chris Weale to beat.
He got round the keeper but, with the goal gaping, put the ball wide.
The Yeovil goal brought more urgency from the Dons, who were looking to build on Saturday's 3-0 victory over Blackpool, but as the game went into three minutes of stoppage-time it looked all over.
Harding picked up a loose ball on the right hand corner of the penalty box and fired a beauty into the far top corner. No keeper could have saved it, but it was a bitter blow for Yeovil, who are wondering if and when their luck will turn.