The Swans put one foot in the Group Stages of the Europa League after a convincing 5-1 win over Romanian side Petrolul Ploiesti at the Liberty.
Wayne Routledge bagged a double while Michu, Wilfried Bony and substitute Alejandro Pozuelo were on target as the Swans were in total control of this Play-Off first leg.
Routledge got the scoring underway after 15 minutes with the winger sidefooting home following Jonjo Shelvey's quickly-taken free-kick.
Michu doubled the advantage after 21 minutes from close range before Routledge added another with a diving header following a pinpoint Pablo Hernandez cross.
After the break, Bony rattled the crossbar just 60 seconds into the half, but he got himself on the scoresheet just before the hour as his effort just squeezed over the line.
Pozuelo added the final Swans goal of the evening, neatly chipping keeper Peterson Dos Santos from 12 yards after a sublime pass from Michu.
Then the Romanian side gave their support something to cheer as Gheorghe Grozav's superb overhead-kick nestled into the corner of the net with two minutes remaining.
It means the Swans head to Romania in seven days' time with a healthy advantage as they look to finish the job and book their spot in the Group Stages.
The Swans made three changes to the starting XI.
Neil Taylor was given the nod at left-back ahead of Ben Davies while Spanish international Pablo Hernandez started on the wing as Nathan Dyer was injured.
Club record signing Wilfried Bony, who came off the bench to score in the home defeat to Manchester United, led the line with Michu offering support behind him.
Jonathan de Guzman, who missed last weekend's defeat to the league champions, had recovered from concussion suffered on international duty to be included among the substitutes.
SWANS: Michel Vorm, Angel Rangel, Chico Flores, Ashley Williams (capt, Jordi Amat, 71), Neil Taylor, Leon Britton, Jonjo Shelvey (Jonathan de Guzman, 69), Michu, Wayne Routledge (Alejando Pozuelo, 60), Pablo Hernandez, Wilfried Bony.
UNUSED SUBS: Gerhard Tremmel, Jazz Richards, Jose Canas Roland Lamah.
PETROLUL PLOIESTI: Peterson Dos Santos, Sebastian Achim, Geraldo Alves, Alexandru Benga, Guilherme, Damien Boudjemaa (Njongo Priso, 57), Ovidiu Hoban (Abel Camará, ht), Sony Mustivar (capt), Gheorghe Grozav, Hamza Younés (Férébory Doré, 57), Filipe Teixeira.
UNUSED SUBS: Mircea Bornescu, Romário Pires, Pablo de Lucas.
The Swans were the first to pose a threat, and a Wayne Routledge cross along the face of goal - following a one-two with Pablo Hernandez - was cleared by a Petrolul defender as Michu was closing in.
But the Swans did find the net after 15 minutes as a quickly-taken free-kick by Jonjo Shelvey was fired in low into the box and Routledge side-footed home from 12 yards.
And six minutes later, the lead was doubled as the Swans took firm control.
On 21 minutes, Shelvey's back-post cross was knocked by the diving boot of Hernandez, and after a slight touch by keeper Peterson Dos Santos, Michu fired into the roof of the net just two yards out.
The Jack Army were still in celebration mode as, on 25 minutes, goal number three arrived.
Michu tracked back and won possession with a sliding tackle, and when Leon Britton sent Hernandez racing down the right, the Spaniard's pinpoint cross found Routledge at the back post, and the winger nodded home with a diving header.
The Swans were in total control, and Routledge almost capped off a perfect half as he latched onto Michu's through ball which sent him in on goal. But the winger's shot beat the keeper but not the crossbar as it deflected over.
Wilfried Bony then steered Hernandez's cross wide from six yards before the half came to a close.
First-half: Swans 3 Petrolul Ploiesti 0
Barely 60 seconds had ticked by when the Swans were launching their first attack of the half, with Hernandez crossing to the feet of Bony, and the striker's first touch allowed him to spin his marker and shoot for goal, only to see his thunderous shot cannon off the woodwork.
Hernandez then fired high and wide after cutting into the box before the Spaniard then teed up Michu on the edge of the area, but his volley deflected just wide for a corner.
But the Swans weren't to wait any longer as they continued their pursuit for a fourth.
In the 58th minute, Routledge threaded through a pass for Michu, and his cut-back found Bony, whose shot squirmed under Dos Santos and crept over the line.
That wasn't the end of the scoring, however, as substitute Alejandro Pozuelo - on for Routledge - coolly chipped over Dos Santos after a sublime through ball from Michu.
Then, with the game coming to an end, Petrolul grabbed a consolation goal in superb fashion.
After Guilherme's cross was deflected, Gheorghe Grozav's excellently executed overhead kick flew past Vorm and into the corner of the net with two minutes remaining.
But that wasn't enough to take the gloss off a result that puts the Swans in an excellent position to progress into the Group Stages.