There has not been too much to cheer about at Molineux in recent weeks, and the sight of a suspended and pensive-looking Matheus Cunha in the stands would have done little to boost the mood.
Everton – looking to increase the 10-point gap between the sides – began brightly, and almost seized the initiative when Abdoulaye Doucouré brilliantly took the ball under control before seeing his effort blocked by Emmanuel Agbadou.
Harrison then drifted an enticing left-footed ball into the box, which narrowly missed the onrushing Beto.
Wolves were having the lion’s share of possession and had their own chances through Rayan Aït-Nouri and Munetsi, but it was the Toffees that struck first.
Harrison broke the deadlock with his first goal of the season when he latched onto Jesper Lindstrøm’s pass and saw his strike take a huge deflection off Matt Doherty before nestling into the bottom corner.
But the hosts fought back before the break, as Jean‐Ricner Bellegarde’s defence-splitting pass was slid home by Munetsi for his first Wolves goal at the end of a slick move from Vítor Pereira’s side.
The Zimbabwe international was withdrawn injured at the break and replaced by Pablo Sarabia, who almost fired Wolves in front when his free-kick from a promising position hit the side-netting.
However, those hoping this would spark a flurry of goalscoring opportunities would be left disappointed, with both sides lacking any sort of cutting edge upfront.
Jørgen Strand Larsen looked to change that narrative after being picked out by Sarabia, but he saw his effort well saved by Pickford.
That seemed to spark the injection of intensity which the contest needed, as Carlos Alcaraz went straight down the other end and teed up Beto, whose shot forced a fine stop from José Sá. Alcaraz was looking lively, showcasing some neat footwork inside the box before firing straight at Sa.
However, the points were ultimately shared in a result that ensured Everton – at least temporarily – move up two places into 14th.
Meanwhile, Wolves stay 17th, but increased the gap between themselves and Ipswich Town to six points. The Black Country side have now only lost one of their eight home league games against the Toffees and remain in a strong position to avoid relegation.
Flashscore Man of the Match: Jean‐Ricner Bellegarde (Wolverhampton Wanderers)