Rafa Benitez's side, missing several key starters through injury, were clear second best in the opening 45 minutes, going in 2-0 down and although they improved in the second half and pulled a goal back through Alex Iwobi they could have few complaints about the outcome.
After a slow start, Wolves are up to seventh having now won four of their last five games and Portuguese coach Bruno Lage is benefitting from the return to full fitness of Mexico striker Raul Jimenez.
Everton, beaten 5-2 by Watford last week, were missing defenders Yerry Mina and Lucas Digne, central midfielder Abdoulaye Doucoure and striker Dominic Calvert-Lewin, and were on the back foot from the start.
The pressure from Bruno Lage's side finally paid off in the 28th minute when defender Max Kilman rose well to power in a header from a Rayan Ait Nouri corner.
Four minutes later, Everton gifted Wolves a second when Ben Godfrey's ill-judged attempted back pass was intercepted by Jimenez, who coolly chipped the advancing Pickford.
Everton came out forcefully after the break and pulled a goal back in the 66th minute when Ben Godfrey's shot into box was blocked by Conor Coady but the ball fall to Iwobi, who reacted well to drill home.
The influential Trincao had a great chance to put the game beyond Everton but pulled his shot wide from close range and Wolves had their keeper Jose Sa to thank when he pulled off a fine reflex save from a Richarlison near post header.
"We don't want to look at the table too much," said Wolves skipper Coady. "We keep moving forward, we want to keep winning games. I thought first half we were outstanding. We wanted to keep that going.
"We knew it would change after half time. We conceded and had to defend but we did it."