Rampant Wanderers netted three second-half goals, but they also had to withstand strong pressure from Vale in an entertaining contest.
Jackett said: "Vale Park is a tough place to come and I'm delighted with the win. I've been here with many clubs and it's never easy, so it's an excellent three points.
"It was nice to score three goals, but the boys also deserve a lot of credit for how they defended. Vale put a lot of crosses into our box and we came under a lot of pressure after going 1-0 up. Our centre-halves were very strong and they had to be.
"I didn't think we got it right in the first half. We were laboured, had too many shots from distance and made too many wrong decisions.
"We addressed that at half-time and were more incisive in the second half. We got the goals to get the job done and I'm very happy."
Leigh Griffiths scuffed the first clear chance of the game in the first minute of the second half, but the striker made amends by opening the scoring in the 56th minute.
Vale defender Carl Dickinson failed to clear his lines and Griffiths stole the ball in a flash before driving a fierce left-foot shot inside Chris Neal's left-hand post from 14 yards.
The home side responded with gusto as Doug Loft's header from Adam Yates' cross struck a post before Dickinson almost atoned when his volley drew a brilliant save from Carl Ikeme.
But Wolves put the game to bed as substitute Bjorn Sigurdarson and the classy Kevin McDonald netted in the 75th and 83rd minutes respectively.
Substitute Ben Williamson also struck the woodwork for Vale late on before Tom Pope headed an injury-time consolation goal which was very much deserved.
Jackett revealed Bakary Sako was left out of his squad after the player admitted he was not in the right frame of mind.
He added: "Bakary has been honest with me. He is aware of the interest in him from other clubs, but we haven't had a bid which is even close to taking him away from us. He has assured me he will give everything for the club if he stays with us and we hope he does stay."