The Shots appeared to be heading out of the bottom two after loanee Dani Lopez, making his first Shots start, broke the deadlock with his first goal in English football on the stroke of half-time.
However the Dons had other ideas and Long's free-kick against the run of play denied Aldershot, who did still move up a place to 23rd with a point.
Danny Hylton enjoyed great opportunities to put Aldershot in front in the first half but he could not direct two free headers on target. Lopez, though, made no mistake in first-half injury time after the Dons failed to clear a corner, denying Neil Sullivan a clean sheet upon his return to Wimbledon.
The Dons started the second half brightly with Jake Reeves narrowly missing the target twice from two early efforts from long range.
Lopez was gifted a clear shot on target by a poor Jonathan Meades clearance but struck straight at Sullivan on the hour mark, before Long's free-kick produced a draw as they clash entered the closing stages.