The Millers appeared to have pulled off a stunning away win as goals from Ben Wiles and substitute Chiedozie Ogbene twice edged them in front, with Jay Rodriguez providing Burley’s reply.

But the Yorkshire side finally succumbed after Cohen Bramall was dismissed for two yellow cards in the 75th minute, setting up substitute Manuel Benson for another late rescue act.

The Belgian had stepped off the bench to provide a goal and an assist and turn around Saturday’s game against Reading, and this time he curled in a lovely effort in the first minute of added time before playing a part in Halil Dervisoglu’s winner in the 10th minute of stoppage time as the Clarets extended their unbeaten run to 16 games.

Burnley's Ian Maatsen celebrates their side's dramatic late winner scored by team-mate Halil Dervisoglu (not pictured) during the Sky Bet Championship match with Rotherham at Turf Moor (Picture: Isaac Parkin/PA Wire)

Rotherham were ahead early when Oliver Rathbone’s pass sent Brooke Norton-Cuffy down the right and his cross to the far post found Vitinho napping, with Wiles, pictured, heading home.

Rotherham defended admirably, and painfully at times, with Lee Peltier hooking Rodriguez’s header off the line, close enough to warrant a goalline technology check, and taking a full-blooded Johann Berg Gudmundsson drive in the groin.

Conor Washington got the better of the two Burnley centre-backs, Taylor Harwood-Bellis and Jordan Beyer, before forcing a fine save from goalkeeper Aro Muric as the Yorkshire side retained a threat on the counter.

The Clarets gradually asserted themselves and were level after 35 minutes. Gudmundsson clipped a cross from a deep position to the left of the box and Nathan Tella reached it and expertly cushioned his volleyed cross over Millers keeper Viktor Johansson and the unmarked Rodriguez scored his ninth of the season.

Rotherham United's Ben Wiles (right) celebrates with team-mates after scoring their side's first goal of the game at Burnley (Picture: Isaac Parkin/PA Wire)

The script seemed to be written for another Burnley win but Ogbene put the visitors back ahead. His first involvement after replacing Hakeem Odoffin was to latch on to a slack pass from Vitinho before firing across Muric and in off the post.

Rotherham dug in but their cause was not helped when Bramall picked up two yellow cards in the space of seven minutes for fouls.

Johansson pulled off a close-range save from Roberts’ diving header but Benson curled a shot into the far corner and set up another tense finish.

And with seconds left on the clock, Benson again attacked the Rotherham left flank and slipped a pass to Josh Brownhill. His shot bounced back off the chest of Johansson and Dervisoglu prodded it home for the winner.

Burnley: Muric, Vitinho (Roberts 74), Harwood-Bellis, Beyer, Maatsen Cork, Brownhill, Gudmundsson (Benson 59), Tella (Dervisoglu 70), Zaroury, Rodriguez (Barnes 74). Unused substitutes: Taylor, Peacock-Farrell, Bastien.

Rotherham: Johansson, Brook Norton-Cuffy (Kelly 86), Peltier, Hall, Harding, Bramall, Odofin (Ogbene 63), Wiles, Barlaser, Rathbone (Wood 77), Washington (Lindsay 63). Unused substitutes: McCart, Eaves, Vickers.

Referee: L Doughty (Lancashire).

'100th minute' - Rotherham United suffer agonising 3-2 loss at Burnley