The visitors had striker Nathan Jarman sent off for a second bookable offence at the end of the first-half, during which both sides hit the woodwork.
Rochdale striker Lee Thorpe hit the post with a header while Adam Rundle did likewise from a free-kick.
But soon after they were dealt a blow as Jarman was dismissed following a lunge on David Perkins – and Rochdale went ahead two minutes into the second-half when Howe headed home Rundle’s cross at the back post.
Howe’s second came in the 55th minute when he collected Kallum Higginbotham’s flick-on and hammered a low drive in off a post.
Andy Taylor’s late header set up a nervous finish, but Howe settled things with his third in time added on.