Cox's solitary strike after 41 minutes settled a dour and scrappy affair at Brisbane Road. O's captain David Mooney crossed the ball into the penalty area and although Shaun Batt scuffed his attempt, the ball fell to Cox and the midfielder blasted the ball home from 12 yards for his eighth goal of the season.
The visitors enjoyed the greater possession but were unable to extend home goalkeeper Jamie Jones.
As Walsall pushed forward, gaps opened up at the back, with Batt and substitute Robbie Simpson both squandered chances to tie up the game.
Tempers became frayed in the final moments with Mooney shown a straight red card after an incident involving Paul Downing, who should have equalised shortly afterwards but he shot high over the cross bar from close range in the last seconds of injury time.