Match ends, Rotherham United 1, Burnley 2.
Sam Vokes' late strike gave Burnley victory over managerless Rotherham.
The Millers, who parted company with Steve Evans on Monday, went behind in the ninth minute as Andre Gray stole in to finish coolly past Lee Camp.
Striker Vokes hit the upright and Camp saved brilliantly from David Jones in a fine first half for the visitors.
Grant Ward levelled with a stunning effort from 25 yards, but Vokes pounced nine minutes from time after Scott Arfield's initial shot was saved.
The victory for Sean Dyche's Clarets moves them up to third in the Championship, while Rotherham, under the leadership of caretaker boss Eric Black, slip a place to 21st.
The hosts, who had conceded 17 goals before the match, showed their defensive frailties for the opening goal as Gray beat Danny Collins to the ball inside the area and fired a low shot into the bottom right corner.
Wales international Vokes almost doubled the lead just after the half-hour as he struck a 25-yard shot against the post before Camp tipped Jones' low effort away.
Rotherham's best effort of the first half saw Burnley goalkeeper Tom Heaton, named in Roy Hodgson's England squad on Thursday, save Matt Derbyshire's low shot.
The Millers were more lively after the break but could not find a breakthrough until a piece of brilliance from Tottenham loanee Ward.
The 20-year-old jinked into a shooting position and sent an unstoppable strike into the top left hand corner.
However, Burnley took all three points when Camp kept out Arfield's strike from point-blank range, but Vokes reacted first to turn the ball home from six yards.
Rotherham caretaker manager Eric Black:
"I will just carry on until a decision [about who will be the new manager] is made. The chairman will make a decision that is right for the club.
"I am here, I am employed by the club, I will go along with that and see where it takes us.
"I just want to go and have a lie down. We are two men down on the training ground which puts a little bit of pressure on. We'll reflect on the game and carry on from there."
Burnley boss Sean Dyche:
"There has got to be credit to them. Sometimes the hardest fight is the one that every thinks you're going to win, but I thought we deserved it overall.
"They kept fighting, they kept pressing, they pressed very hard, they gave everything to try and win. They get a worldy out of the blue and all of a sudden it's 'what's gone on there?'
"I am delighted with the mentality of the players; it rubs off on each other."
- 20RawsonSubstituted forBroadfootat 77'minutes
- 4CollinsBooked at 61mins
- 33SmallwoodBooked at 65mins
- 22NewellSubstituted forWardat 71'minutes
- 24AndreuSubstituted forMaguireat 71'minutes
- 19Clarke-HarrisBooked at 90mins
- 21BoydSubstituted forTaylorat 76'minutes
- 7GraySubstituted forLongat 88'minutesBooked at 90mins
- Peter Bankes
- Shots on Target
Second Half ends, Rotherham United 1, Burnley 2.
Chris Long (Burnley) is shown the yellow card.
Chris Maguire (Rotherham United) wins a free kick in the defensive half.
Foul by Matthew Taylor (Burnley).
Delay over. They are ready to continue.
Jonson Clarke-Harris (Rotherham United) is shown the yellow card for a bad foul.
Delay in match Joey Barton (Burnley) because of an injury.
Foul by Jonson Clarke-Harris (Rotherham United).
Joey Barton (Burnley) wins a free kick in the defensive half.
Attempt missed. Jonson Clarke-Harris (Rotherham United) left footed shot from outside the box is just a bit too high. Assisted by Grant Ward.
Attempt missed. Danny Ward (Rotherham United) right footed shot from outside the box is close, but misses to the left. Assisted by Chris Maguire.
Substitution, Burnley. Chris Long replaces Andre Gray.
Offside, Rotherham United. Grant Ward tries a through ball, but Danny Ward is caught offside.
Attempt missed. Chris Maguire (Rotherham United) left footed shot from outside the box is high and wide to the left.
Attempt blocked. Jonson Clarke-Harris (Rotherham United) left footed shot from outside the box is blocked. Assisted by Matt Derbyshire with a headed pass.
Danny Collins (Rotherham United) wins a free kick in the defensive half.
Foul by Andre Gray (Burnley).
Offside, Rotherham United. Jonson Clarke-Harris tries a through ball, but Danny Ward is caught offside.
Goal! Rotherham United 1, Burnley 2. Sam Vokes (Burnley) right footed shot from the centre of the box to the bottom right corner.