Match ends, Swansea City 1, Rotherham United 0.
Striker Bafetimbi Gomis scored his first goal for Swansea City as they eased past Rotherham United into the third round of the League Cup.
The 29-year-old slid a shot past Scott Loach after a neat turn inside the box to put the Premier League side ahead.
Rotherham's best chance fell to Alex Revell, whose effort was blocked by the sliding Kyle Bartley, and after that the visitors rarely threatened.
Problems with the turnstiles meant kick-off was delayed by 10 minutes.
Swans boss Garry Monk made 10 changes to the team that beat Burnley 1-0 on Saturday, giving debuts to Federico Fernandez and Tom Carroll.
It was Swansea who had the better of the first half before Gomis found the bottom right-hand corner after the Frenchman worked himself into a shooting position.
Championship outfit Rotherham did put the home side under pressure from set pieces and throw-ins, but without stretching the Swans defence.
Ecuadorian winger Jefferson Montero hit the side netting after a well-worked corner in the second half for the hosts, who face West Bromwich Albion in the Premier League on Saturday.
Swansea entertain Everton in the third round.
Swansea manager Garry Monk: "All strikers want to score and Bafe has that. The goal will give him confidence but he put in a very good shift.
"What we learned from Burnley was we knew the aerial bombardment was coming.
"The best way to control that is by us keeping the ball and we managed to do that in the second half when the long balls that were coming in were spread out."
Rotherham assistant manager Paul Raynor: "I'd like to think we can leave with our heads held high.
"We've come up against a very talented Swansea team and apart from the last 10 minutes I think we created some good chances. If we were a bit more ruthless we might have gone into extra-time."
- 30SheehanSubstituted forG Sigurdssonat 59'minutes
- 56FultonSubstituted forShelveyat 45'minutes
- 14CarrollBooked at 82mins
- 18GomisSubstituted forBonyat 74'minutes
- 4Ki Sung-yueng
- 23G Sigurdsson
- 20MorganBooked at 90mins
- 4ArnasonBooked at 41mins
- 5BroadfootBooked at 48minsSubstituted forBrindleyat 55'minutesBooked at 63mins
- 19SadlerSubstituted forSkarzat 71'minutes
- 23TidserSubstituted forNewtonat 58'minutes
- Steve Martin
- Shots on Target
Second Half ends, Swansea City 1, Rotherham United 0.
Corner, Swansea City. Conceded by Richard Brindley.
Jonjo Shelvey (Swansea City) wins a free kick in the attacking half.
Foul by Kári Arnason (Rotherham United).
Attempt missed. Wilfried Bony (Swansea City) right footed shot from long range on the right is close, but misses to the right.
Federico Fernández (Swansea City) wins a free kick in the attacking half.
Foul by Jordan Bowery (Rotherham United).
Craig Morgan (Rotherham United) is shown the yellow card.
Wilfried Bony (Swansea City) wins a free kick in the defensive half.
Foul by Craig Morgan (Rotherham United).
Foul by Jonjo Shelvey (Swansea City).
Alex Revell (Rotherham United) wins a free kick in the defensive half.
Attempt missed. Conor Newton (Rotherham United) right footed shot from the centre of the box is too high.
Attempt missed. Wilfried Bony (Swansea City) right footed shot from the centre of the box is too high.
Corner, Swansea City. Conceded by Richard Wood.
Attempt blocked. Wilfried Bony (Swansea City) left footed shot from the centre of the box is blocked.
Tom Carroll (Swansea City) is shown the yellow card.
Foul by Tom Carroll (Swansea City).
Kári Arnason (Rotherham United) wins a free kick in the attacking half.