Wolves condemned Everton to a third successive Premier League defeat as Max Kilman and Raul Jimenez scored in a 2-1 win at Molineux on Monday.
Bruno Lage’s side took control in the first half thanks to Kilman’s first ever Wolves goal and a clinical finish from Jimenez.
Alex Iwobi reduced the deficit in the second half, but Wolves held on to extend their unbeaten run to five league games.
With four wins in that impressive streak, Wolves have climbed to seventh, while Everton dropped down in 10th.
Everton has won just one of its last six league games to shatter the optimism created its four-match unbeaten start to Benitez’s first season in charge.
Radamel Falcao was held scoreless as Rayo Vallecano’s winning run at home was halted by Celta Vigo in the LaLiga.
The result ended Rayo’s five-match winning streak at its Vallecas Stadium this season, keeping the promoted Madrid club in sixth place, five points behind leader Real Sociedad after 12 matches.
Bologna moved up to mid-table after beating last-placed Cagliari 2-0 in Serie A.
Premier League: Wolves 2 (Kilman 28, Jimenez 32) bt Everton 1 (Iwobi 66).
LaLiga: Rayo Vallecano 0 drew with Celta Vigo 0; Levante lost to Granada 3 (German 7, Suarez 38, Puertas 69).
Serie A: Bologna 2 (De Silvestri 49, Arnautovic 90+6) bt Cagliari 0.