It looked as if Michael Smith's header was going to give the Dons their first win in six games only for them to be denied by Reid, who backed up his Boxing Day brace at Oxford to net his fourth goal in three games.
Lewis Alessandra forced AFC Wimbledon goalkeeper Ross Worner into action from 25 yards before Luke McCormick made a good block to deny Smith after Charlie Sheringham put him through at the other end.
Smith took his goalscoring tally for the season into double figures in the second minute of the second half as he rose to head in Peter Sweeney's cross from the left.
Plymouth only began to rally in the game's latter stages, with Worner having to make a strong save to stop Reid's long-rang effort with eight minutes remaining.
But the Pilgrims rescued a point in the 88th minute when a brilliant ball by 17-year-old Ben Purrington picked out Reid and the Pilgrims' top scorer did well to finish from a tight angle.