Howell's 56th minute goal did the trick for the Daggers on their home patch as they upset the promotion-chasing Robins.
It was Howell's eighth goal of the season and first for six games as John Still's battling side ended a frustrating run of three matches without a win.
Victory was also the Daggers' first win over Cheltenham in their six previous meetings while defeat for Mark Yates' side ended an impressive five-game unbeaten run.
Shaun Harrad forced a smart stop out of keeper Chris Lewington as the visitors, looking for their first npower League Two victory since early December, started brightly while at the other end Sam Williams was denied by Scott Brown.
Ben Strevens, Medy Elito and Williams all had first half chances as the hosts pressed hard for an opener before Howell rifled into the top right-hand corner to give them a deserved lead.
Just ten minutes later the home side were awarded a spot-kick when Steve Elliott fouled Matthew Saunders. Up stepped Williams but his placed penalty in the bottom corner was saved by Scott Brown.
Darren Carter shot wide of a post as the visitors went close to equalising, but Still's men held on for a welcome win.