Bradley Dack scored the game’s only goal, as he rose well to head past goalkeeper Jamie Jones from Doug Loft’s corner after 14 minutes.
On-loan Millwall striker John Marquis came the closest to adding a second for the hosts, who are now mathematically safe from relegation, but his header from Brennan Dickenson’s cross was cleared off the line by Ashley Eastham.
Dale, who have now lost three of their last four away games, were reduced to 10 men when Jones was sent off for fouling Cody McDonald in the 63rd minute.
Matty Lund, making his first start for Dale since Boxing Day, was dismissed seven minutes later for a foul on Dack.
Leading scorer Ian Henderson had their best chance when he hit the post shortly before the break with a deft chip.