Robert Grant headed home the opener just before the break and Michael Symes doubled the visitors' advantage with a 30-yard wonder strike midway through the second half and although Chris Dagnall gave Rochdale hope with a 91st-minute effort, Accrington held on for a deserved victory.
Coleman said: "It's been frustrating waiting so long to get a win against Rochdale, even in the six games we've had against them since returning to the Football League. But I had a bit of a feeling about this game because the last time we were down this way we beat Oldham away.
"Rochdale are a very good side, possibly not at their best on the day, especially in the first half, but they put us under a lot of pressure in the second half.
"We didn't deserve to go in ahead at half time, but there have been plenty of occasions here when we've deserved more than we've got and we didn't play anywhere near as well as we can in the first half.
"We were sweating on the bench for the last five minutes when Dagnall scored, but to see it out and win was fantastic."