After a week that had seen some of their players not paid and fresh doubts raised about the take over of the club by Sulaiman Al Fahim, Yebda's first goal for Pompey in the 19th minute could not have been better timed.
Wolves' boss Mick McCarthy had warned his players that the clash with troubled Portsmouth would be their most dangerous match of the season so far.
It was a warning they failed to heed as they slipped to their fifth defeat in eight Premier League games.
But they had enough possession and created enough chances to have taken something from the game only for Portsmouth to record their first away win since last November at Sunderland - a run of 17 games.
Wolves dominated for spells in the second half after the introduction at the interval of striker Sylvan Ebanks-Blake and winger Michael Kightly, who had strong appeals for a 63rd minute penalty rejected when Marc Wilson appeared to handle his cross.
David James then denied Greg Halford three minutes from time with a stunning save before Ebanks-Blake lifted the rebound over the bar from six yards to perfectly sum up Wolves' frustration.
Ultimately, McCarthy's side were the architects of their own downfall as they had been given a scare seconds before on-loan Benfica midfielder Yebda struck the decisive blow and they paid the price for not taking that on board.
Following a Jamie O'Hara corner, Tal Ben Haim had his shot blocked and Tommy Smith saw his drive deflected over the bar.
Wolves again failed to deal with a second successive corner from O'Hara and when the ball found its way to Kevin-Prince Boateng, his cross was headed home by the unmarked Yebda from just four yards.
Wolves were fortunate not to fall further behind nine minutes later when only a smart one-handed save by Wayne Hennessey low to his right denied Aruna Dindane.
Wolves should then really have been on level terms on the stroke of half-time, only for James to save from Matt Jarvis and then Ben Haim to block a goalbound drive from Kevin Doyle.
The arrival of Ebanks-Blake and Kightly gave the Wolves attack more momentum, but they could not find a way past James, as Jarvis had an effort deflected wide and Halford and Christophe Berra both failed to hit the target with headers.