Joel Byrom set Graham Westley's troops on their way seven minutes before the break while David Amoo pounced moments later to double Preston's advantage at Deepdale.
Ed Upson's sending off for a late challenge on Byrom and Preston defender Chris Robertson's header made progression certain in the second half.
It was the hosts who struck first through Byrom, with the midfielder calmly firing past Glovers' goalkeeper Marek Stech.
And moments later it was two as neat Preston interplay carved the Yeovil defence apart and allowed Amoo to race clear and round Stech.
Two goal-line blocks kept it 2-0 at half-time before Upson's dismissal on the hour paved the way for a powerful Robertson header in the 70th minute to seal the deal.