The win took Mahmudullah’s men to the top of the points table with five wins in six matches, while Rangpur slumped to their third defeat in seven matches on Thursday.
The Riders had put up an ordinary show with the bat, posting 104 for 9 before rain held up play for about an hour during the chase with the Bulls on 25 for 1 in 3.3 overs.
The target was then revised to 75 in 13 overs as Mahmudullah led his team to the win with an unbeaten 23 with three balls to spare.
They lost Evin Lewis (4), who scored a century in the last match, to a leg-before decision early on before drizzle began at the Zahur Ahmed Chowdhury Stadium in Chittagong.
After play resumed, the spinners removed Rony Talukder (23) and Mehedi Maruf (3) to give their team a glimmer of hope but Mahmudullah and Nadif Chowdhury (16) steadied the ship and settled in to snuff out any chance of a Riders comeback.