Gary McDonald's close-range finish set up a second-round clash with Coventry, as the Shrimps moved into the second phase of the competition for the first time in four years.
It was the second time Morecambe had claimed victory over Dale at Spotland this season, following their 2-1 league success in October.
Bentley said: "It's a fantastic result for everyone at the club and it was nice to come here and win for the second time in a matter of weeks.
"When we had to dig in, we did it well, and I don't remember our goalkeeper having too many saves to make.
"We defended well, put our bodies on the line when we had to and got the all-important goal away from home and kept a clean sheet."