A Luke Moore brace and a Danny Graham strike was enough to send the Swans into the Capital One Cup third round with this 3-1 win over Barnsley at the Liberty.
Graham got the ball rolling on 23 minutes as he chested home Moore's header from a yard out, before Moore himself got into the scoring act in the second half from close range.
Barnsley made a spirited comeback, and Bobby Hassell headed them back into contention before he rattled the crossbar soon after.
But Moore ended the contest in the 88th minute as he beat keeper Ben Alnwick from an acute angle following good work from substitute Mark Gower.
The Swans made seven changes from the starting XI, with club-record signing Ki Sung-Yueng and Kyle Bartley making their debuts while Ben Davies made his first start after his sub appearance against West Ham at the weekend.
Gerhard Tremmel, Alan Tate
, Kemy Agustien and Luke Moore also made their first starts of the season.
Gerhard Tremmel, Angel Rangel (Jazz Richards, 56), Alan Tate
(capt), Kyle Bartley, Ben Davies, Kemy Agustien, Ki Sung-Yueng (Mark Gower, 73), Jonathan de Guzman, Nathan Dyer, Luke Moore, Danny Graham (Stephen Dobbie, 56).
Subs not used:
Michel Vorm, Ashley Williams, Michu, Leroy Lita.
Ben Alnwick, John Stone, Bobby Hassell, Scott Golbourne, Scott Wiseman (capt), Martin Cranie, Stephen Dawson, Tomasz Cywka, Chris Dagnall, Craig Davies (Marlon Harewood, 63), Jacob Mellis (Jordan Clarke, 63).
Subs not used:
Luka Lidakevicius, Danny Rose, Stephen Foster, Kelvin Etuhu, Lee Collins.
The Swans took a while to get into their stride as the visitors settled into the contest early on.
Tomasz Cywka drove straight at Gerhard Tremmel before Jacob Mellis' effort failed to trouble the German keeper soon after.
The Swans' first real effort came in the 22nd minute as Ben Davies and Nathan Dyer linked up before the winger's cross was met by the head of Danny Graham, but a timely block kept his effort out.
But the Swans were not to be denied as seconds later they were ahead. Angel Rangel's cross to the back post was nodded back by Luke Moore, and Graham chested home from a yard out.
The lead was almost doubled minutes later as Graham teed up Nathan Dyer, whose thunderous 20-yard effort was tipped wide by keeper Ben Alnwick after a fine reaction save.
From Jonathan de Guzman's corner, Kyle Bartley rose highest but couldn't keep his header from rising over the crossbar.
Barnsley responded, Cywka controlled Tremmel's punched clearance from a corner before unleashing a dipping volley. Tremmel reacted well to get down low and collect a tricky shot with relative ease.
The Swans retaliated with a Moore header, but his effort curled just past the far post from Rangel's excellent cross.
HALF-TIME: Swans 1 Barnsley 0
Neither side made inroads during the early stages, and Michael Laudrup made the first changes ten minutes into the half as Jazz Richards and Stephen Dobbie replaced Rangel and scorer Graham.
And the changes paid off as Richards was immediately into the thick of things, beating his marker before crossing low to Moore in the box, who controlled before his shot on the turn found the top corner from eight yards.
It prompted Barnsley boss to make a double change of his own as Jordan Clarke and Marlon Harewood came on for Mellis and Craig Davies.
And the small visiting support were soon cheering as a Scott Golbourne cross found Bobby Hassell, and his header crept into the corner of the net.
It set up a tense 20 minutes at the Liberty, with the visitors looking to push on and get themselves level.
And the visiting fans were up on the feet again as Chris Dagnall dispossessed Bartley some 40 yards out, and the ball spurted towards goal, but Tremmel raced out of goal to snuff out the striker's attempt.
Laudrup then called time on Ki Sung-Yueng's home debut as he was replaced by Mark Gower for the remaining 17 minutes.
Barnsley pushed again and this time they went within inches of levelling as Hassell's powerful 25-yard drive cannoned back out off the crossbar.
The Swans needed a response, and they almost settled the contest as some good work again by Richards saw Dobbie push on, and his pass to Moore saw the striker in on goal but under pressure from two defenders. He managed to get an effort in, but that bounced off Alnwick and a defender.
Seconds later, though, the game was settled. Excellent work by sub Gower saw him close down an attempted clearance from the visiting defence. The loose fell to Moore who, from a very acute angle, slid his effort low past Alnwick with two minutes left.