It was a perfect pick me up for the South Coast club after a turbulent week in which some of their players were not paid on time despite new owner Sulaiman Al-Fahim's plans for a £150 million cash injection.
They also went into the game on the back of the worst top-flight sequence of results at the start of a campaign since Manchester United in 1930.
But Pompey deserved their first success of the campaign and Wolves boss Mick McCarthy's claim his side were facing "their most dangerous game of the season" proved well founded.
Yebda, a French-born Algerian international, impressed in midfield while Tommy Smith was always a handful for the Wolves defence and worked tirelessly.
Wolves had a decent amount of possession and were unfortunate not to be given a second-half penalty, but they often struggled to find any rhythm despite the promptings of Matt Jarvis in the centre of the park.
Wolves began brightly and a long throw from Greg Halford was met by Christophe Berra whose flicked header flew straight at Pompey keeper David James.
But Portsmouth were not afraid to knock the ball around despite their disastrous start to the campaign.
Kevin-Prince Boateng had their first worthwhile effort on goal, spinning to fire in a shot from a narrow angle which Wolves keeper Hennessey turned around the post.
Jarvis brought the home fans to life with a powerful 50-yard run and he was allowed to surge into the box as the Pompey players backed off.
But he would have been disappointed with his eventual low shot which James dealt with comfortably.
At the other end Aruna Dindane was only just too high with a 25 yard shot on the turn and Tommy Smith had a low shot cleared off the line by Jarvis.
But after 20 minutes Portsmouth took the lead through Yebda.
Boateng was the creator with a right-wing cross and Yebda was perfectly positioned to head past Hennessey into the corner of the net.
Wolves were stunned by this reversal and it needed a fine save from Hennessey to prevent Portsmouth from doubling their lead.
Smith played the ball into the path of Aruna Dindane and his first time effort was turned aside by Hennessey at full stretch away to his right.
The rebound broke to Smith who cut back inside to make a better angle but drilled his shot across the face of goal.
Wolves began to get a foothold back in the match and a well worked free-kick move ended with Foley crossing to Doyle whose shot was deflected just wide.
Wolves fans were becoming frustrated but James produced a fine reflex save to deny Keogh at point blank range in first half injury-time and then Doyle's follow-up shot was blocked.
McCarthy responded to his side's first half performance by bringing on last season's top scorer Sylvain Ebanks-Blake and Michael Kightly in place of Keogh and Foley.
Portsmouth had the first chance of the second period when Dindane's back header from Smith's cross was saved by Hennessey.
But Wolves looked more purposeful and Jarvis had a shot deflected wide after racing on to a pass from Doyle.
From Jarvis's resulting corner, Halford got up well but could only direct his header wide of the far post.
Kightly and O'Hara became the first players to be booked by referee Howard Webb after a flare-up in the Portsmouth penalty area.
Wolves looked to be denied a clear-cut penalty when television replays clearly indicated Pompey defender Marc Wilson had handled a right-wing cross from Kightly.
Boateng was yellow-carded for a foul on Henry and Halford curled the resulting free-kick just wide.
James then beat out a powerful drive from Halford with Blake putting the rebound over the bar.