Paul Pogba, skipper Davide Petrucci and Joshua King all had good chances to put the Reds in front, but two Jason Lowe goals and one from Grant Hanley gave Rovers the win and booked their place in the last 16.
United, meanwhile, moved top of the Premier Reserve League with a 1-0 win over Bolton with a David Gray strike.
Source: Manchester Evening News
Source: M.E.N.