Adam Chapman justified manager Chris Wilder's faith in retaining him in the side, despite several others vying for his central role, by drilling home a low 22-yard shot in the 33rd minute from James Constable's lay-off.
However, substitute Mekki struck six minutes from time to hand Shots a vital point.
The U's might have added further goals before the break, but both Alfie Potter and Sean Rigg sliced their shots in front of goal.
The Shots came back into it in the second half and Danny Hylton had two good opportunities to equalise.
The striker glanced a header wide from a free-kick, and then squandered a chance at the far post.
Dan Lopez also went close with a difficult left-foot volley from eight yards.
Aldershot did level, though, five minutes from time when substitute Mekki headed over goalkeeper Ryan Clarke.
Oxford's Simon Heslop was sent off a minute from the end for a professional foul.
Before kick-off, both teams joined the spectators in a minute's applause for former Oxford player Mitchell Cole, who died last week aged just 27.