Goals in either half sealed the win for the Conference outfit.
The hosts took the lead early on when a free-kick was tapped to Lawson D'Ath on the edge of the box. The Eastleigh man strode up to the ball and drilled it beyond the dive of Wes Foderingham.
In a first half where the home side arguably had the better of the chances, Swindon came closest when a cut-back from the right picked out Nathan Byrne on the edge of the area. The full-back made a firm connection but struck the ball high over the crossbar.
After the break, Town started to come to life following a number of changes in personnel. Nathan Thompson picked up possession on the halfway line and drove at the heart of the Eastleigh defence but his fizzing effort cannoned back off the upright.
George Barker then moved away from his marker before skewing a shot wide and Matt Jones drove a shot into the side-netting after his overlapping run was found by Barker.
Before the end, substitute Lee Marshall reacted well to clear the ball off the line after Wes Foderingham had been beaten by a goal-bound effort.
Seconds before the final whistle, McAllister added Eastleigh's second of the evening when his header found the corner of the net despite the efforts of Foderingham to keep it out.
