Boss Sean Dyche called for one final push from Everton after they snatched a dramatic point in their fight for survival.
The equaliser, in the ninth minute of stoppage time, cancelled out Hwang Hee-chan’s first-half opener.
Everton – two points above the drop zone – host Bournemouth on the final day of the Premier League season but face a nervous wait to see if they will start the game in the bottom three.
“I was really pleased with the mentality of the players. There’s no excuses from me, no excuses from them,” said Dyche, who confirmed Dominic Calvert-Lewin and Nathan Patterson suffered hamstring injuries.
“This is the challenge right in front of us. I told them that at half-time. It’s not about shapes and tactics, it’s about mentality.
“I’m really pleased for them, we all got the reward for putting in a proper shift and trying and never losing the belief we could score.
“We need it for next week, quite obviously, but it’s a mentality which has grown and I’m very pleased with that side. It shows a strong sign of what the group has become.
“There was a lot of noise around the club (when Dyche arrived in January) and we calmed that a little bit. There was a lot of noise about the team, we missed some important players – one being Dom so there was a lot of noise about him.
“There have been a lot of challenges, I’m not bothered about making excuses. So what can we do? It wasn’t about ‘woe is us’ it was about ‘what can we do to affect this game?'”
Everton started well with Calvert-Lewin twice going close before getting caught on the break for the opener after 34 minutes.
Abdoulaye Doucoure’s pass was seized on by Adama Traore who raced 70 yards, brushing off Amadou Onana’s challenge and forcing Jordan Pickford into a smart save – only for Hwang to gobble up the rebound.
Calvert-Lewin, who had been battling a groin problem, then limped off in stoppage time to add to Everton’s problems.
Wolves had a degree of control and Pickford needed to save from Matheus Nunes as the game entered nine minutes of stoppage time.
Everton threw men forward and it eventually paid off in the final seconds.
“Yes, a lot (of injury time). It was the first time I have seen it in the Premier League,” said Wolves boss Julen Lopetegui, who has guided the team to a mid-table finish.
“It’s done, it was a pity. Nine minutes is a lot but they scored the goal in the time, we have to defend better.
“It’s football, we won at Everton in the last minute and today we lost two points. Maybe we deserved to win more here than there. It wasn’t easy to play this kind of match, against a team who are fighting to survive. It’s a final for them.”
Striker Raul Jimenez was denied a possible farewell appearance as an unused substitute before walking down the tunnel before full-time.
Lopetegui added: “He was not happy but I always try to be honest with the players. You can’t make all the things perfect as a coach. You have to take the emotion out of the situation.”