An entertaining first half was illuminated by two goals in the space of two minutes. The Grecians struck first on 29 minutes when Jamie Cureton lashed home from 12 yards after good work by Richard Duffy, but Tommy Miller levelled things up almost immediately from Tommy Spurr's corner kick.
Exeter stepped it up a gear after the break and went in front when Liam Sercombe chested the ball down 25 yards from goal and unleashed a stunning volley that dipped over the head of Nicky Weaver and into the net.
Three minutes later, it was 3-1. Ryan Harley chipped the ball into the box and as the Wednesday defence failed to clear their lines, Scott Golbourne lashed home his first goal for Exeter.
The Grecians were rampant and after Cureton and Harley had spurned good opportunities, Cureton slotted in his second of the game on 72 minutes after a fine flowing move from back to front.
Another fine move ended with Exeter getting their fifth two minutes from time. John O'Flynn controlled well before firing into the bottom corner to claim an emphatic win for the stylish Grecians.