The Ducks levelled on 43 minutes when Kevin Davies escaped his marker to send a bullet header into the roof of the net from Peter Mead's corner.
However, Wellingborough regained the lead on 52 when Atkinson was sliced down in the area by Trevor How and Dave Liddle fired in the penalty.
United battled back well to put the visitors under pressure, but they defended well until finally cracking in the 84th minute when How converted a deep cross at the far post to earn a point.