Bakary Sako held his nerve to convert a penalty six minutes from time to settle a tight match after Shrewsbury winger Jon Taylor was sent off for handling Matt Doherty's goalbound header.
It ensured there was to be no happy ending for Shrewsbury manager Graham Turner, who had been looking to claim the scalp of Wolves, a club whose fortunes he revived during a seven-and-a-half-year spell in charge between 1986-1994.
"My first impressions was it was a definite penalty and a red card, and obviously the referee thought the same," Jackett said.
"Leigh (Griffiths) went off with a bad ankle but we had a few players who would be happy in that situation to take that pen. It was such a crucial time and a crucial decision so I was pleased there was a player of the quality of Sako to put the ball away."
Jackett was especially delighted with the three points, in front of a record crowd of 9,510 at Shrewsbury's Greenhous Meadow, after Wolves had tasted League One defeat for the first time this season in midweek when they lost at home to local rivals Walsall.
"We're pleased with where we are and that we haven't let the sides at the top of the league get away from us. We're in there," he said.
"We also think we need to improve and we're looking to improve, both internally and externally as the season goes on. We are a work in progress and certain areas we do have to improve.
"But this was a massive game for Shrewsbury and you could see that from the capacity crowd. The atmosphere is something we had to overcome - and overcome it we have."