Here is Paddy’s verdict on Daniel Farke’s side, who cashed in on a calamitous day for the chasing pack with another Teemu Pukki match winner and another clean sheet.
• Tim Krul
Watching brief for the most part. Had to react sharply to paddle away Lewis Wing's inswinging early corner. Clearly had his arm grabbed for Rotherham's disallowed goal. Luck was in when Ben Wiles' fearsome shot clipped the top of his bar. Another clean sheet. 7
• Max Aarons
Hard to over emphasize how big that late block was from Matt Crooks. Those two extra points could be massive. Seemed to lose his bearings when bursting onto Kenny McLean's raking diagonal ball in the first half. Numerous runs into the Millers' box, first half especially 8
• Grant Hanley (C)
Switched to the left hand side of the defence in Ben Gibson's absence. Not a bother to the captain. Decisive aerial work in the fraught final moments. Stepped into midfield to spark a flowing move that ended with Todd Cantwell's miscued shot. 7
• Christoph Zimmermann
Pressure was on after an emergency call up following a long spell on the substitutes' bench. One loose piece of play in possession did not prove costly prior to the interval. Glancing near post flick cleared off the line. Unfussy, dependable, reliable. 7
• Dimitris Giannoulis
Energy and drive were a key outlet to release some of the Rotherham second half pressure. Lovely body swerve and balance turned defence into attack on more than one occasion. 7
• Kenny McLean
Came into his own when it turned into something of an arm wrestle second half. Athleticism required to get about the park and pile up the tackle count. Superb spot for Max Aarons' first half dart. 7
• Oliver Skipp
His maturity is off the richter. Even when it got tense in the second half, constantly showing for the ball in tight areas and the composure to play through the lines. Unflustered. 8
• Emi Buendia
Just another assist for the growing collection. For him, a golden chance in the 38th minute from Mario Vrancic's cutback but his effort clipped Clarke Robertson. Prior to that dancing feet to back heel a ball for Teemu Pukki to sidefoot tamely at Viktor Johansson. Perfect weight and timing of the pass for Todd Cantwell from a Grant Hanley-inspired counter. 8
• Mario Vrancic
That goal will not come. Although it is not for the want of trying. Quick feet and the power but just lacked a touch of direction from the edge of the area in the fifth minute. Pulled a big chance wide in the 10th minute when left unmarked. Turned provider for Emi Buendia. Dragged another later effort from a Pukki rebound wide. 7
• Todd Cantwell
Brave on the ball in the second half despite the close attentions of Rotherham defenders. Failed to find the finish to match a flowing move when Buendia squared it invitingly for his late-arriving run. Quality spot for Pukki to double his tally in the 82nd minute. 7
• Teemu Pukki
Red hot and oozing confidence. Had plenty of time and acres of space but the end result was never in doubt when he burst clear to draw Millers' keeper Johansson and fire through his legs for his fourth goal in eight days. Could easily have a hat-trick on another day, with two sidefooted efforts saved by Johansson. His movement triggered panic in Rotherham's defence. 8
City substitutes
• Lukas Rupp (for Cantwell, 90+1) n/a
• Adam Idah (for Pukki, 90+4) n/a
• Alex Tettey (for Vrancic, 90+6) n/a
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