Marco Stiepermann's 84th-minute goal at Carrow Road condemned Swansea to just a second league defeat of the season in a game that was full of chances for both sides.
It was just the second Championship match this season in which the Welsh side failed to score, so Steve Cooper will hope that that clinical edge is restored when his team return to familiar surroundings.
They have won 10 points from a possible 15 at the Liberty Stadium this season, while only Middlesbrough have conceded fewer goals at home than Swansea (three).
That is not good news for Rotherham, who have not won on the road since they beat Wycombe Wanderers 1-0 on the opening weekend.
That is one of just two victories in the Millers' last 53 away games in the Championship, while they have not won at Swansea since April 2006.
Despite being without a number of key players, Rotherham put in a spirited performance to grind out a result – something they have struggled to do in their recent spells in the second tier, which will give Warne confidence that his team can avoid an immediate drop back to League One.
Swansea City Championship form: DDWWDL
Rotherham United Championship form: DLWLLW
Andre Ayew and Marc Guehi both returned to Swansea from international duty early due to fatigue and are doubts for the game.
In better news for Steve Cooper, Ben Cabango is available again having missed the last two matches with a hamstring injury.
There was a concern that Kyle Naughton may be set for a spell on the sidelines after he was forced off against Norwich with a hamstring problem, but he is also available for selection.
Kieran Sadlier became the latest addition to Rotherham's ever-growing injury list when an ankle problem forced him off against Preston. It is expected to rule him out for around three months.
Jamal Blackman missed the Preston match with an ankle knock and returned to parent club Chelsea for treatment during the international break, but could be back available for the trip to South Wales.
Joe Mattock is also back in contention following a hamstring issue, but Paul Warne may not risk the left-back, who has a patchy injury record.
Swansea City possible starting lineup:
Woodman; Naughton, Bennett, Cabango; Roberts, Fulton, Grimes, Smith, Bidwell; Lowe, Gyokeres
Rotherham United possible starting lineup:
Blackman; Olosunde, Ihiekwe, Wood, Harding; Wiles, Lindsay, Barlaser; Jozefzoon, Ladapo, Crooks
We say: Swansea City 1-0 Rotherham United
Even if they are missing Andre Ayew, Swansea should still overcome a Rotherham side with plenty of injury problems of their own. Paul Warne's men have rarely been outplayed this season though, and they should give a good account of themselves at the Liberty Stadium.