All Sergio Agüero can do is keep offering the kind of performance that was essential to this victory over Huddersfield Town. The Argentinian scored twice to follow the two he registered against Monaco in Manchester City’s previous outing.

The display was capped by him pressing furiously just before being replaced towards the end. This caused enthusiastic applause from his manager, Pep Guardiola, who had previously dropped Agüero and who might have preferred Gabriel Jesus for this replay but for the Brazilian’s metatarsal injury.

Yet, following this canter into the FA Cup quarter-finals, the Catalan showered him with praise. “It’s the best Sergio Agüero ever. The performance was amazing,” Guardiola said. “The runs were at the right moment and the right tempo. It is the best performance I’ve ever seen from Sergio in many things. He is good with the ball, one against one, two against one. He scored two goals – when he plays in that level Sergio is unstoppable.

“His performance was top – the same with Claudio [Bravo], his performance with the foot helped us build up.”

Regarding his goalkeeper, Guardiola was surely doing what all managers do: protect players, even when they misfire. This was the case yet again for Bravo as he allowed Harry Bunn’s seventh-minute shot to go under him and into the net. He was also cheered ironically by his own supporters when collecting the ball safely.

Asked about this, Guardiola said: “Ask the fans, the performance from Claudio was amazing, to make the build-up, nobody else can do that. He reads when the men are free. It’s not easy to read that.

“He gave us the opportunity to play. What the fans express, I’m not here to judge them.”

Pressed if he might be concerned about the reaction to him, Guardiola said: “No, he’s strong enough. He’s one of the best. This year he was named as one of the best five goalkeepers in the world. But I know how the media works. I’m delighted and so happy he’s with us. I know I can count on him. I can count on his behaviour when he’s playing and when he’s not playing. I just congratulate him on how he played at Huddersfield and how he played today.”

Guardiola is yet to decide if Bravo will displace Willy Caballero for Sunday’s trip to Sunderland. The Argentinian has become the No1 and the head coach said: “Now I make a good dinner, I am going to sleep with my wife. Tomorrow I’ll decide on Sunderland.”

City’s last game had been that 5-3 thriller here with Monaco, meaning a break of just over a week. Four of those days were spent in the warmth of Abu Dhabi, where Guardiola met the owner, Sheikh Mansour, for the first time.

The trip recharged mid-season batteries yet still City slumbered as Huddersfield, who had made nine changes, took the lead through Bunn. Next there were twin penalty appeals that involved the same player, Jon Stankovic, going to ground and seeming to handle inside the area. The first time Kevin De Bruyne swerved inside and wrong-footed the defender, who appeared to touch the ball with a hand. A little later it was Raheem Sterling who tried a cross and again looked to have seen it deflected by Stankovic’s digits. On both occasions, though, the referee, Paul Tierney, was not interested.

Later, after City had equalised, the official did point to the spot and once more Jankovic was the culprit, the No27 pulling Nicolás Otamendi to the floor in the 33rd minute. Up stepped Agüero to rifle in his 21st goal of the season.

City’s earlier goal had come from some slick Sterling work. With half an hour played the winger took the ball along the right, and four or five dazzling step-overs later Tareiq Holmes-Dennis required a lie down and the ball into Leroy Sané left the German an open goal.

Agüero’s penalty was followed by Guardiola’s side going 3-1 up with 38 minutes on the clock. This time the Argentinian was provider: after his fierce shot was beaten out by Joel Coleman, Agüero retrieved the ball and squared to Pablo Zabaleta and the right-back rolled home his second of the season.

City’s fourth arrived on 72 minutes. This was fashioned in pinball-style as Fernandinho found Zabaleta who found Sterling and his instant delivery was smashed past Coleman by Agüero. A few minutes later Agüero pressed from the front, forcing the ball to be punted back to City and now came the hands-over-his head applause from his manager. Following Kelechi Iheanacho’s late fifth, Guardiola surely felt the same regarding his side’s performance. It was professional and impressive.

Agüero said: “I always try to do my best and do what the manager wants me to do. I want to make my manager happy with my performances.”