Wilson, 22, signed as a £3million replacement for Lewis Grabban, who joined Norwich in June, was denied a hat-trick by a late penalty miss, but apart from that the former Coventry ace proved a cut above.
Cherries boss Eddie Howe hailed his two-goal hero, saying: "He did really well in pre-season and he has continued that form.
"It's always important for a striker to start well at a new club and he will improve and develop from here. This will give him a big lift."
Howe has been allowed to splash the cash this summer and said no-one was guaranteed a first team shirt.
"We intend to rotate the squad this season," he said. "When you look at the squad, with everyone fit, we could pick two teams and there wouldn't be much between them.
"This was the best start possible and we need to build on that, and I think we will."
Bournemouth caught Huddersfield cold with a goal after just 24 seconds. Charlie Daniels put Matt Ritchie in down the right and his cross was first controlled and then dispatched past Alex Smithies by Pugh with two touches from close range.
Wilson scored his first in the 32nd minute when he collected Tommy Elphick's through ball, held off Joel Lynch, who claimed he was fouled, and fired home.
Five minutes after the restart Yann Kermorgant made it 3-0 reacting first to the rebound after Smithies saved Pugh's header and Wilson added his second in the 64th minute from Ritchie's cross.
Smithies was forced to bring down Wilson just inside the box in the 76th minute but the keeper made amends to save to his left to deny Wilson his first league hat-trick.
Howe said: "We made the best possible start to the game and after that we were the dominant team and I am pleased with the win.
"The clean sheet means as much to me as the four goals and we need to build on this and hopefully we can."
Many Huddersfield fans left the ground after the fourth goal and boss Mark Robins admitted: "It was poor. It was difficult to explain and sometimes that is what happens in sport.
"It was the first game of the season when everyone is in great spirits and this puts a real dampener on it. I will fight but it's really disappointing because we have worked hard over pre-season."
Fans booed Town off at the end and Robins added: "The supporters having a go at me or the players are the same ones who cheer us when things go right. They want to be entertained and we have to give them that.
"The players have to grow up and take responsibility. The system we play only works when the players put a shift in and too many players decided to take a day off.
"It's still early days and we dump this result in the waste bin and move on."