The O's dominated the first-half and might have opened their account on 20 minutes when Syam Ben Youssef had a shot cleared off the line.
The opening goal came after 32 minutes when diminutive midfielder Cox ran onto a downward header from Kevin Lisbie and delivered a powerful volley from 20 yards. The ball hit Dale defender Stephen Darby and bounced down and over his goalkeeper Matt Edwards.
Four minutes before half-time, Orient youth player Odubajo marked his first league start with a wonder goal. He cut inside two defenders and unleashed an unstoppable drive from 25 yards.
The visitors improved after the break with the introduction of winger Nicky Adams, who was transfer listed this week, but it was Gray who gave his side hope when he waltzed past a couple of defenders before sliding the ball home from 10 yards.
However, the O's responded and finished the stronger with Cox having a couple of late shots turned away for corners, leaving the bottom of the table visitors to reflect on a run of 14 away matches without victory.