Diogo Jota scored a stunning acrobatic volley as the Wolves defeated Armenian Pyunik 4-0 in Molineux's 8-0 lead.
Jota came off the bench late for an excellent finish from Raul Jimenez.
Pedro Neto opened the game with a debut before Academy member Morgan Gibbs-White scored a cross.
Ruben Vinagre made it 3-0 from close range before Jota hit.
The 8-0 aggregate victory is the largest of the wolves in Europe, meaning that they are only two games away from the Europa League group stage.
In Serie A against Turin, which defeated the Belarusian FC Shakhtyor 6-1 overall, there will be a tougher test. The two games against the Italians take place on 22 and 29 August.
The wolves are entering Europe for the first time since 1980 and have recorded their biggest ever continental victory in Armenia last week with a 4-0 victory in Armenia.
This result allowed them to talk more relaxed about the return leg at Molineux, and it is not surprising that manager Nuno Espirito Santo made the changes.
Only Skipper Conor Coady and Joao Moutinho kept their places off the side that ended with Leicester in their Premier League debut, while Jesus Vallejo, Neto and Patrick Cutrone all had their full debuts.
The lack of urgency was in the first half for the most part no chance, and only in the second half succeeded the wolves to score their first goal. Gibbs-White hit the Pyunik goalkeeper directly.
But that chance seemed to bring the hosts to life, and any glimmer of hope that Pyunik had from an unlikely comeback ended with a devastating 10-minute break in which the hosts scored three goals and could have achieved more.
After the score was 3-0, Nuno may have been tempted to tell his players to let go. Instead, the striker Jota and Jimenez were committed.
And they both scored a sensational goal as Jimenez picked up the ball for Jota for a stunning volley.
The wolves felt comfortable in their first season in the Premier League when they finished seventh. But the addition to compete in Europe this time is an additional challenge – a crowded schedule list.
Due to their progress in the play-off round, they face five games in only 16 days until September 1st.
What they said
Wolf boss Nuno Espirito Santo: "It was not easy, Pyunik got off to a great start again, I talked to her coach and I wish her all the best for the future."
"I thought all my players did a very good job, not just the new players, the second half was very good.
"It was a good game and I think we started the game normally because some players take more time, and we showed a better performance over time and the second half was very, very good."
"I am satisfied with the whole team, all players have done a very good job."