Wilson, a £3million buy from hometown club Coventry, first barged Town's Joel Lynch out of the way and coolly netted after 32 minutes.
The 22-year-old played on as Huddersfield tried to claim a foul by the right touchline before cutting inside and drilling low past keeper Alex Smithies.
Wilson's second goal, from a Pugh cross, saw a weak close-range shot after 64 minutes squirm under Smithies. Between Wilson's two strikes Yann Kermorgant had scored in what was already a miserable afternoon for Terriers fans.
Wilson joined the Cherries as a replacement for star striker Lewis Grabban, who was sold to Norwich in the summer.
His second goal prompted a walk-out by some home fans, who booed and chanted "you don't know what you're doing" at boss Mark Robins during a woeful display.
Wilson even fluffed the chance of a hat-trick when he missed a penalty on 76 minutes after Smithies brought him down. Lynch left Smithies in trouble with a poor back header and the keeper caught Wilson in the box with his trailing leg.
Smithies was booked for the foul but redeemed himself by diving to his left to hold on to Wilson's tame spot-kick.
Bournemouth, beaten 5-1 by Huddersfield a year ago, made an electric start to the season when Pugh struck before the season was one minute old.
Charlie Daniels put Matt Ritchie in down the right and his cross was first controlled and then dispatched past Smithies by Pugh with two touches from close range.
Slick Bournemouth, whose team featured three of the same back four humiliated a year ago, never looked back. Wilson took his two goals and in between Kermorgant had made it 3-0 on 50 minutes.
Smithies parried a headed from Pugh but Kermorgant lashed in the rebound from close range.
Huddersfield's only had two real chances in the game. The first came on 39 minutes when Oliver Norwood rattled the bar from 35 yards from Jonathan Hogg's pass.
The second came from home debutant Matt Crooks, a 20-year-old academy product, who forced keeper Lee Camp to tip over a header from a Norwood corner on 62 minutes.
Other than that Huddersfield, who played an unfamiliar 3-4-1-2 formation, were hardly in the game.
In fact it could have been worse for the Terriers. Ritchie twice went close early in the game and then nearly scored with a spectacular 75-yard lob on 41 minutes after a mistake by Smithies.