James Baxendale's 25th-minute goal made it two league victories out of two for the Saddlers, who also won through to the second round of the Capital One Cup in midweek.
Oldham, who had won their opening league game 4-3 at Stevenage, had shouts for a penalty waved aside when Cristian Montano's shot appeared to strike a hand.
Walsall duly made the most of their luck as Baxendale fired home from 10 yards after Oldham's defence failed to clear an Adam Chambers cross.
Oldham's troubles continued when centre-back David Mellor was injured in the opening half and Montano did not return at the start of the second period.
The hosts huffed and puffed but lacked a cutting edge as James Dayton, Adam Rooney and substitute Sidney Schmeltz all blazed over.
The Latics' biggest attacking threat was centre-back James Tarkowski, who had a goalbound shot blocked by Chambers and a header well saved by Richard O'Donnell.