Match ends, Swansea City 1, Rotherham United 0.
Swansea City secured a third successive home win over a blunt Rotherham United thanks to Matt Grimes' first-half goal.
Grimes claimed a first goal of the season as his speculative effort went straight through goalkeeper Jamal Blackman, who endured a tough afternoon.
Jamal Lowe and Jake Bidwell were both denied by last-ditch blocks as they looked to add gloss to the scoreline.
Rotherham saw a late penalty claim for handball by Ryan Bennett turned down.
Swansea rise to fourth in the Championship, two points off top spot, while Rotherham are 19th.
The visitors opted to name only seven substitutes despite the rule change this week which means a bench of nine is permitted, with injuries forcing boss Paul Warne's hand.
Rotherham were hoping to end a rotten recent record in Swansea, having won just one of their last 16 trips in the league.
However, it was arguably a good time to be facing the Swans as injuries and illness forced boss Steve Cooper into making four changes from the side narrowly beaten by Norwich before the international break.
Key players were missing at both ends of the pitch in defender Marc Guehi and talisman Andre Ayew, with the Swans suffering a further blow with forwards Viktor Gyokeres and Jordon Garrick absent having returned positive Covid-19 tests.
That meant a first league start for 21-year old Liam Cullen, the academy graduate who happened to be a mascot for the club when they played Rotherham in 2006.
It was Cullen who produced the best chance of a tepid opening 15 minutes when he met Grimes' corner and headed firmly at goal, but Blackman showed fine reactions to save.
Blackman did not play in Rotherham's win over Preston, with Viktor Johansson starting in goal, and the decision to recall the Chelsea loanee backfired when Swansea opened the scoring with a gift of a goal.
Blackman allowed Grimes' effort from 20 yards to squirm through his body after an unconvincing punch from a Connor Roberts corner.
Blackman then received a huge slice of luck after charging out of his goal and missing his kick, with Roberts' cross presenting an open goal for Lowe, who incredibly hit the post from just 12 yards out.
Rotherham's best move came moments before the interval, but Freddie Woodman was able to save as Jamie Lindsay twisted and fired in a low shot from just outside the penalty area.
The Millers made two changes at the break, including the introduction of a Miller, with Matt Olosunde and Jamie Lindsay making way for Trevor Clarke and Mickel Miller, while Michael Smith and Kyle Vassell were also thrown on early in the second half as Warne rang the changes.
However, it was the hosts who enjoyed the first chance of the second period but Cullen took too long to shoot.
Rotherham were only really asking questions from set-pieces, but it was Swansea who almost doubled their lead from a free-kick as Blackman tipped Yan Dhanda's effort away.
Rotherham captain Michael Ihiekwe headed over under pressure from Kyle Naughton with 20 minutes remaining but the Swans really should have killed off the game when Blackman was again out of position and Jake Bidwell had a free strike at goal, but Wes Harding made a superb block.
Bidwell then headed just wide and the hosts became nervous having failed to add a second, with Vassell heading at Woodman as Rotherham poured on the pressure late on.
Warne's men were aggrieved in the final moments when Smith's header was cleared off the line by Bennett, with the visitors convinced the former Wolves defender used his arm to control the ball, but referee Matthew Donohue waved away the protests.
Woodman then dropped a corner with just 90 seconds remaining, but Korey Smith scrambled clear when any Rotherham touch would have led to a goal, while Angus MacDonald fired over deep into stoppage time.
Swansea boss Steve Cooper told BBC Sport Wales:
"I am really happy with it, it was a hard-fought game, we created some really good chances that we could and should have done better with.
"We scored a scruffy goal to be fair and to show the other side of the game in the second half, showing resilience and character and dealing with the set-pieces and having the kitchen sink thrown at us, I'm really happy with that.
"It is the games and the days like this that could be really important. I am not saying we wouldn't have won this game last year, but there were games like this we didn't win.
"Also credit to the boys because our record after the international break hadn't been great, we do lose a lot of players to the international break. I am really pleased with the win as these are difficult games."
Rotherham boss Paul Warne said:
"In fairness to Swansea I thought they played really well and asked us a lot of questions and we didn't have the answers for everything. I thought our first-half performance was lacklustre, and it just wasn't us.
"The joy of having five changes is good when things aren't going great, and it allowed us to make a couple of changes at half-time and then tweak the system.
"We caused them more problems and on another day we might have got a penalty or a tap-in from the goalkeeper's drop, but Swansea could have scored more as well.
"I'm not trying to sugarcoat it, they were the better team today and they get the three points."
- 2BennettBooked at 32mins
- 21DhandaSubstituted forPalmerat 77'minutes
- 20CullenSubstituted forRoutledgeat 73'minutes
- 9LoweSubstituted forSmithat 87'minutes
- 22OlosundeSubstituted forClarkeat 45'minutes
- 16LindsaySubstituted forMillerat 45'minutes
- 26BarlaserBooked at 45mins
- 28JozefzoonSubstituted forVassellat 62'minutes
- 9HirstSubstituted forSmithat 54'minutes
- Matt Donohue
- Shots on Target
Second Half ends, Swansea City 1, Rotherham United 0.
Attempt missed. Kyle Vassell (Rotherham United) left footed shot from outside the box misses to the left. Assisted by Angus MacDonald.
Attempt missed. Angus MacDonald (Rotherham United) right footed shot from the left side of the box is too high. Assisted by Matt Crooks with a headed pass following a set piece situation.
Foul by Kasey Palmer (Swansea City).
Trevor Clarke (Rotherham United) wins a free kick on the right wing.
Corner, Rotherham United. Conceded by Jay Fulton.
Attempt missed. Mickel Miller (Rotherham United) right footed shot from the centre of the box is too high. Assisted by Ben Wiles with a cross following a corner.
Corner, Rotherham United. Conceded by Connor Roberts.
Substitution, Swansea City. Korey Smith replaces Jamal Lowe.
Offside, Swansea City. Matt Grimes tries a through ball, but Wayne Routledge is caught offside.
Corner, Rotherham United. Conceded by Ben Cabango.
Attempt blocked. Michael Smith (Rotherham United) header from the centre of the box is blocked. Assisted by Kyle Vassell with a cross.
Offside, Swansea City. Kyle Naughton tries a through ball, but Jake Bidwell is caught offside.
Attempt saved. Kyle Vassell (Rotherham United) header from the left side of the box is saved in the bottom left corner. Assisted by Trevor Clarke with a cross.
Corner, Rotherham United. Conceded by Jake Bidwell.
Foul by Ryan Bennett (Swansea City).
Michael Smith (Rotherham United) wins a free kick in the defensive half.
Attempt missed. Kasey Palmer (Swansea City) right footed shot from long range on the right misses to the left.
Offside, Swansea City. Matt Grimes tries a through ball, but Jamal Lowe is caught offside.