The outcome was never in doubt after Swansea scored three goals in 11 first-half minutes courtesy of a Wayne Routledge double and a Michu strike.
An own goal from Petrolul keeper Pecanha, who inadvertently diverted a Wilfried Bony shot into his own net after it had squirmed under him, and an effort from substitute Alejandro Pozuelo made it 5-0.
Gheorghe Grozav got a stunning consolation for the Romanian cup holders with an overhead kick, but it appears unlikely to spark a remarkable turnaround in the tie.
Laudrup has said from the start of the European campaign that the minimum he wanted to achieve was a place in the group stage, and knows they are one professional performance away from that target.
He said: "To score five goals and win 5-1 is excellent. In the first half-hour we did very well, we kept the ball and moved them around.
"We scored three of our goals, we could have scored more, and we gave them nothing.
"I told the players at half-time we had the chance to go for a fourth goal and we did that.
"They were more offensive in the second half but we still dominated, got the fourth and a great fifth from Pozuelo.
"We still have to finish the job, after the first leg against Malmo I said we still had a job to do and that is the same here.
Source: PA
Source: PA