A deflected Ryan Williams goal was enough to secure the Shrimps a first ever Football League win at the Pirelli Stadium after losing on their four previous visits.
And to complete a miserable afternoon for the hosts, defender Shane Cansdell-Sherriff was sent off in added time.
After the 1-0 win, Morecambe manager Bentley said: "It's not been a happy hunting ground for us in the past but we've shown loads of desire and determination to come here and get a result after losing our last two.
"These things go for you or against you and today it was our turn for a bit of fortune. Kevin Ellison had a shot and it hit Ryan on the backside and went in the opposite corner.
"It's a fantastic result for us because, in my eyes, Burton are one of the favourites for promotion.
"They'd won the last three without conceding a goal so we knew we were coming into a tough game.
"I think once we got our lead, the game plan went as we wanted. We sat in a bit in the second half and hit them on the break and I thought with a bit more quality we could have had a second goal."