North End struck twice in the opening few minutes of a rescheduled first round tie as they coasted to a first away win since January.
The only black mark was the sending off of Eddie Lewis six minutes from time after receiving a second yellow card in the aftermath of Preston's fourth goal.
Lewis sprinted down the left wing before crossing for substitute Simon Lynch to score, but was then booked after running towards the travelling fans.
Mansfield's only joy came in the 65th minute when keeper Kevin Pilkington saved Graham Alexander's twice taken penalty after David Artell had handled on the edge of the area.
Mansfield got off to a terrible start when Preston striker Richard Cresswell - once on loan at Field Mill - headed in Lewis' third minute corner.
North End, fielding six internationals despite missing nine first-team players through injury, were then gifted a second goal by referee Phil Prosser just six mins later.
The referee booked Mansfield midfielder Adam Murray for encroaching at a free-kick even though Preston had clearly played the ball.
He ordered the kick to be moved forward 10 yards to the edge of the area and with a strong wind behind him, Alexander curled the set piece around the wall and into the bottom corner.
There were no complaints in the 31st minute when Alexander's 30-yard cross-field ball found Omar Daley who beat Alex Baptiste before sliding in Preston's third goal.
Mansfield tried to mount a second-half fight-back with the strong wind now in their favour and Rhys Day twice went close with headers in the first five minutes of the half.
In-form Colin Larkin, with seven goals in seven games, almost grabbed a late consolation when he headed an Alex Neil cross against the foot of the post.