Just weeks after a league defeat to the Toffees, Wolves had some respite from their top flight troubles with cup action and Marshall Munetsi gave them a first half lead after an improved performance.
Everton brought on the cavalry and pushed for an equaliser, but Wolves should take confidence from standing firm.
They booked their place in the next round with a fantastic late goal from Tolu Arokodare – his first for the club – to add shine to the win.
Analysis
Vitor Pereira made nine changes to the Wolves side that lost to Leeds last time out.
In a half empty Molineux with little atmosphere to speak of, the opening 15 minutes on the pitch were just as dull.
Wolves – surprisingly utilising a makeshift back four – had plenty of possession and looked after the ball fairly well with Andre as a midfield pivot, but neither side created many chances.
Everton had a brief opening when they broke forward and Tyler Dibling had a sight of goal, but he fired high and wide.
The Toffees came closest when Michael Keane had a free header from a long throw-in, but Sam Johnstone pulled off a top save.
Beto of Everton is challenged by Santiago Bueno (Photo by Clive Mason/Getty Images)
Despite those chances, it was Wolves that took the lead after 29 minutes. Jhon Arias forced Mark Travers into a strong save from an audacious volley and Munetsi was on hand to follow up for his first of the season.
Wolves were controlling the game well and had another chance when Jorgen Strand Larsen was on the stretch but still forced Travers into a save, as they took their lead into half-time.
Wolves started the second half fairly well too but as Everton brought on reinforcements from their bench, they began to wrestle control.
Jack Grealish of Everton is fouled by Jhon Arias (Photo by Clive Mason/Getty Images)
A superb deep Jack Grealish cross was met by Jake O’Brien at the far post, but it fell kindly for Johnstone to collect.
Santi Bueno then brought down Grealish just outside the box and was booked for his troubles. James Garner smashed the crossbar from the resulting free-kick.
Garner then had another effort from the edge of the box as Everton pushed for an equaliser, but Johnstone got down well to make the save.
Wolves wrapped up the win with Arokodare’s first goal for the club in the 87th minute. Joao Gomes released the striker down the right channel and he lifted the ball over Travers with an excellent finish.
That added shine to the Wolves win, as they moved on to the fourth round.
Key Moments
GOAL 29 Munetsi follows up to put Wolves ahead
GOAL 87 Arokodare chips the goalkeeper to wrap up a Wolves win
Teams
Wolves: Johnstone, Doherty, S.Bueno, Krejci, H.Bueno, Bellegarde, Munetsi (J.Gomes, 81), Andre (Agbadou, 87), Hwang (R.Gomes, 68), Arias (Toti, 81), Larsen (Arokodare, 68).
Subs not used: Bentley, Hoever, Wolfe, Lopez.
Everton: Travers, O’Brien, Tarkowski, Keane, Coleman (Mykolenko, 78), Garner, Iroegbunam, McNeil (Ndiaye, 59), Alcaraz (Dewsbury-Hall, 45), Dibling (Grealish, 59), Barry (Beto, 45).
Subs not used: King, Patterson, Aznou, Gueye.