Wolves had five Portuguese players in their team - Patricio, Moutinho, Neves, Helder Costa and Jota - a Premier League record.
Everton included only Richarlison of their six senior new arrivals, with Lucas Digne on the bench and Kurt Zouma, Yerry Mina, Bernard and Andre Gomes not considered ready.
Richarlison was perfectly placed to prod home the opening goal in the 17th minute after Boly and Cenk Tosun had tussled in the air for Leighton Baines' free kick and the loose ball bounced off Boly.
Nuno Espirito Santo's side were given the chance to haul themselves back in the game four minutes before the break when Jagielka was sent off.
The former England defender had a poor first touch from a pass across the back which allowed Jota to dart in. Jagielka brought him down with a lunging challenge which caught the Portuguese around the shins and referee Craig Pawson had no hesitation in quickly producing a red card.
Neves unleashed a superb, curling effort into the top corner of the net from the resulting free kick 20m out to bring Wolves level and almost lift the roof off Molineux.
Everton regained the lead in the 67th minute with another goal from Richarlison. This time, the 21-year-old ran away from Neves on to a short, square pass from Tosun before neatly curling the ball beyond Patricio.
Wolves remained composed, however, and continued to probe for a second equaliser. And they were rewarded with another quality goal in which Neves had a heavy influence 10 minutes from time.
The playmaker dug out a sublime, pacy cross which just needed the slightest touch from Jimenez to send it flying high into the net, again giving keeper Jordan Pickford no chance.