Maximilian Kilman scored his first Wolves goal and only his second professional career goal to put the Wanderers ahead before Raul Jimenez's elegant chip doubled their lead only a few minutes later.
Alex Iwobi scored his third Premier League goal for Everton, incidencially all three have come against Wolves, in a spirited second half performance but they couldn't find a equalising goal.
Story of the match
Following their home humiliation against Watford, Rafa Benitez made four changes, including the reintroduction of forward Richarlison. Mason Holgate, Jean-Philippe Gbamin and Alex Iwobi were also restored to the starting line-up in place of Lucas Digne, Tom Davies and Anthony Gordon.
The home side made a positive start to the encounter and should have scored after 10 minutes. Neves struck a volley from the corner of the penalty area from a Moutinho corner and forced a smart save out of Jordan Pickford.
Their good start looked like it was going to be rewarded when Hwang curled the ball into the bottom corner from close range. Jimenez's trickery drive into Everton's penalty area saw the ball make its way to the South Korean, but VAR ruled the goal out for offside.
Wolves did eventually take the lead after 28 minutes, through an unlikely goalscorer. Defender Kilman leapt the highest in a congested area from Rayan Ait-Nouri's corner to break the deadlock.
The goal opened the English defender's account for the club on the 44th time of asking.
Everton's woes went from bad to worse four minutes later through a defensive howler from Ben Godfrey. The centre-back, who was playing at left-back, saw his poor backpass picked up by Jimenez.
The Mexican striker calmly chipped the ball over Pickford to score his first goal at Molineux in over a year and double the Wanderers' lead.
Fabian Delph replaced Gbamin at half-time and Benitez's side improved in the second half. Demarai Gray failed to make the most of two separate opportunities before Richarlison failed to capitilised on a Jose Sa error.
With 25 minutes remaining, Everton halved the deficit. A long distance strike by Godfrey caused confusion amongst the Wolves backline and Iwobi's crisp finish was too quick for Sa.
Ironically, it is Iwobi's first Premier League goal since the Toffees' 2-1 win at Molineux last season.
The game told the story of a match of two halves, as Wolves struggled to control the play as easier as they did in the opening 45 minutes.
Academy graduate Anthony Gordon thought he had rescued a point for his side when his header seemed destined for the back of net, only for Sa to be alert to palm the ball away and deny the 20-year-old his first professional goal.
Victory lifts Wolves to seventh in the Premier League table, four points off West Ham United in the Champions League spots. Whilst Everton remain in 10th after suffering their fourth defeat of the campaign.