Wolves won in Europe for the first time in 39 years but boss Nuno Espirito Santo was not pleased with the performance against Besiktas.
The game at Vodafone Park looked to be heading for a goalless draw until Willy Boly wrote his name into club folklore with a stoppage-time goal in Istanbul.
The big defender was on hand to score with a finish befitting of a striker rather than a centre half. Ruben Neves floated a ball over the top of the home defence and Boly took a touch before turning and firing the ball past Loris Karius, who smacked the pitch in frustration afterwards.
The goal ensured Wolves were off the mark in this season's Europa League, having been beaten at home by Braga last month, and gave the club its first win in European football for almost exactly 39 years.
Wanderers' last success came in the UEFA Cup on October 1 1980, when a Mel Eves goal gave them a 1-0 win against PSV Eindhoven at Molineux.
Nuno admitted the result had been celebrated briefly, but he was not happy and said: "It was good and in the end we are happy. We had two minutes of celebration only.
"The goal gives us a victory in a tough, tough stadium but we needed more moments of talent.
"We gave too many chances to Besiktas and sometimes today we didn't attack as a unit, it was more individually. So we have to improve.
"We have a lot of things to improve. We won but we must be better, better in how we play and grow. Why did some players not play so well? We must find the why.
"We made substitutions to try and find solutions, because we were not good. We had to find solutions from the bench and change the dynamic of the game."
Boly's goal was reward for a much-improved second-half performance from Wolves having ridden their luck at times during the Group K clash, especially in the first 45 minutes when Besiktas hit the woodwork.
With Braga and Slovan Bratislava drawing 2-2 in Portugal, it puts Nuno's side right in contention just a point behind the other teams in the group.
However, the Wolves boss was only thinking about the Premier League and Sunday's trip to the Etihad Stadium to face champions Manchester City.
"The next game is Sunday, not until next time do we think about the group stage," he said. "We are already recovering because on Sunday we play. It is a long, long season – Thursday, Sunday, Thursday, Sunday."
Besiktas are bottom of Group K with no points from their opening two matches and have won only once in all competitions so far this season, increasing the pressure on manager Abdullah Avci.
Avci was in charge at Istanbul rivals Basaksehir for five seasons before his appointment at Vodafone Park in the summer, during which time the club has become one of the top teams in the Turkish Super Lig.
Asked about his job, he replied: "I believe that we will turn this situation around and I believe our fans will keep pushing us, because we need their support.
"We are working on things. We tried hard from the beginning until 90 minutes and my players gave everything, they left everything on the pitch.
"We also missed some of our players through sickness and injury."
