In a thrilling opening five minutes, Ched Evans was close to opening his account from the game's first attack when he struck a post after a clever short corner routine.
Kevin McDonald quickly levelled the contest with a cushioned volley from the edge of the area and the Blades pulled clear with two goals in the space of three minutes midway through the first half.
Evans fired them ahead with a 20-yard effort before Lee Williamson tapped into an empty net after Dave Lucas had parried another Evans strike.
Evans doubled his personal tally with another clinical finish before the interval and skipper Michael Doyle claimed the fifth with a long-range shot in the 52nd minute.
Temitope Obadeyi reduced the arrears with a neat finish in the 68th minute but by that stage the contest was long since over.