Keith Hill's men had to play a patient game against John Ward's well-organised Pirates, who went close to taking the lead in the opening 45 minutes when Lee Brown's near-post effort was pushed away by goalkeeper Josh Lillis.
The home side, however, started to exert control in the closing 15 minutes of the first half with Joe Rafferty's cushioned volley the closest they came to scoring.
Ian Henderson fired over the top early in the second half but the deadlock was broken on 58 minutes when Rafferty's cross from the right was cleverly flicked home by Hogan.
Four minutes later Dale doubled their advantage, on-loan Blackburn youngster Jack Connell releasing Cummins and the striker slamming a firm finish past Steve Mildenhall in the Rovers goal.
Michael Smith drove a shot into the side-netting as the visitors refused to buckle in the closing stages, but Rochdale held on comfortably for a win that moved them to within a point of League Two's summit.