Rovers had struggled before the break, but according to their manger Ronnie Moore deserved to progress for their performance after the restart.
"We were slow out of the blocks. They're a nice footballing side and if you let them run in the space we gave them in the first half then you're going to be under pressure," he said.
"They had a great chance where their lad hit the outside of the post, but in the second half we got to grips with them and they were nowhere near the threat they were in the first half.
"What you want now is a nice home draw. Anything can happen on the night in this competition. It would be nice to get to the final."
The rest of the second round ties will be played on Tuesday night, including Scunthorpe against Grimsby Town at Glanford Park.