Dayton fired home with his left foot after making space just inside the box to give manager Lee Johnson a deserved point on his return to his former club.
Jay Emmanuel-Thomas had fired City in front with an acrobatic left-footed volley from Ryan Taylor's 36th-minute cross after a good move down the left involving Bobby Reid.
But the home side also owed their interval lead to goal-saving tackles by Scott Wagstaff and Brendan Moloney, to deny Dayton and Adam Rooney respectively, after the dangerous Jonson Clarke-Harris had set up both chances.
Reid was just wide for City after 23 minutes, while Oldham's James Wesolowski had a shot blocked by Marlon Pack just before the break.
Emmanuel Thomas's goal was his 11th of the season. Neither goalkeeper had many saves to make, but Oldham had the edge on possession for most of the game.