Latics' boss John Sheridan was at a loss fathoming out another desperate defensive performance, which has left his side clinging to the sixth spot in League One.
Sheridan hauled off first-choice keeper Les Pogliacomi last week and he probably thought about doing the same thing to his stand-in Alan Blayney, when he gifted Maynard the opening goal in the 25th minute.
Blayney and centre-half Sean Gregan made a mess of a routine back-pass and allowed the young striker to roll the ball into an empty net from the right of goal.
Crewe could have had more goals in a one-sided first half. Ryan Lowe failed to get the ball under control after taking it around Blayney and he also had an effort chalked out for offside after Maynard fired a shot onto the post.
Oldham were without leading scorer Chris Porter, who was nursing a knee injury and it showed as Luigi Glombard and Paul Warne got very little change out of a resolute Crewe defence.
Visitor's wingman Paul Edwards did cause problems on the left and after racing passed Danny Woodards he set-up Warne, but the striker rapped the underside of the bar with his shot.
Oldham improved after the break but Lowe should have extended Crewe's lead when he was put through by Mike O'Connor, only to drag his shot past the far post.
Maynard showed him how it was done when Lowe set him up in the 71st minute and he put the ball confidently under Blayney for the second.
Richie Wellens handed the visitors a lifeline with five minutes to go, his crashing left-foot drive hit the top corner, following substitute Andy Liddell's free-kick.
Crewe held on fairly comfortably for a deserved win and their first against a top six side this season.