Good work from Jake Nicholson down the left, his driven cross turned around the post for a corner.
Under no pressure, Tom Harte tried to guide the ball back to Dye but only succeeded into wrong footing the keeper and the ball rolled into the net to complete the scoring.
Substitute Shaun Pendleton went inches wide with a long-range effort and then Nicholson raced clear but Dye did well to turn his stinging drive over the bar.
AFC Mansfield now look forward to the tough trip to Hemsworth MW on Saturday to complete their 8 game away run.
AFC Mansfield: Wright, Wilson, Dudley (Madin 65), Allott, Austin, Hughes, Williams (Nicholson 63), Patterson, Fearon, Karkach, Plummer (D’Laryea 68). Subs not used: Annable & White.
Referee: Joe Goodwin (Leeds)
Assistants: Steven Lennon (Sunderland) & Ronan Coller-Booth (Leeds)
MoM: Ollie Fearon