Rochdale went ahead after Reuben Hazell was penalised for a shove on Craig Dawson and, after Gary Jones slammed the resulting penalty against a post, O'Grady converted the rebound.
The former Latics striker grabbed his second after seizing on a woeful back pass by Hazell and calmly slotting inside the far post from 10 yards, however, Dale were forced to hold on when Scott Wiseman was sent off for a foul on Cedric Evina, then Dean Furman halved the deficit.
"Chris despatched an unbelievable finish for his first goal and, although the second came from an Oldham mistake, it was still a super finish," said Hill.
"We defended really well until Oldham scored, which made it a bit nervy but we deserved the three points.
"Craig Dawson has matured into an unbelievable player at the back and Marcus Holness is doing very well next to him so we were able to withstand the pressure. I can't remember Oldham having many clear-cut chances. We had a game plan and it worked."