In these early Rodri-less days Manchester City lack the stranglehold the peerless No 6 offers, so Pep Guardiola, as promised, is finding solutions. This time there was a two-goal show from Mateo Kovacic, who, operating in the Spaniard’s berth, equalled his goal tally of last season with an equaliser then City’s second.

But the champions are far more open, as Andreas Pereira’s opener and Rodrigo Muniz’s 88th-minute finish for Fulham illustrated, along with other passages, as during the second half when their keep-ball ended with Josko Gvardiol flinging himself to the ground to block Raúl Jiménez’s effort near the penalty spot.

Muniz’s goal, too, came as City were played through. Emile Smith Rowe passed right to Reiss Nelson, who relayed the ball to the Brazilian and he made no mistake.

And while Jérémy Doku’s canny shoulder-dip and move inside to his right to allow a thumping right-foot finish proved decisive, the measure of City’s discomfort was in the contest ending with them in quasi-holding-on mode, plus Ederson going into the book for slow play and his manager for subsequent sarcastic applause.

The early menu consisted of a cornucopia of City chances. Ilkay Gündogan slipped Erling Haaland in, but Bernd Leno saved the shot. Gündogan ran through but his attempted steer with his left boot went wide. Haaland did the same – missing to the right. Rico Lewis was upended by Sasa Lukic, Bernardo Silva was City’s draught-excluder in Fulham’s wall, and Haaland smashed the free-kick into him. Ouch.

From here, City lost their thread. Kovacic, Jack Grealish and Lewis were clumsy, the last of these particularly wayward when allowing Adama Traoré’s burning pace to gain the wrong side. Suddenly the No 11 was shooting, though Ederson’s legs saved his team.

Easy, maybe, to read this all a corollary of Rodri’s absence but firm evidence came in Pereira’s finish. First, City might well have been shifting the opposition around via the Spaniard’s subtle link-play, thereby keeping Fulham from possession. Second, he would have stopped Marco Silva’s side foraging down the left and switching right. Instead, Jiménez fashioned a wonderful backheeled cross and Pereira volleyed in.

A carbon copy nearly followed. Another stray Grealish pass allowed Jiménez to feed Pereira. The No 18 sprinted 60 yards along the right and found Alex Iwobi, who teed up Traoré in front of goal. But as Ederson advanced, the No 11 stabbed high.

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Silva could not believe the miss. His men soon paid. After ranging downfield, City claimed a corner and from this the ball dropped to Kovacic. An instant hit sprayed off a Joachim Andersen leg, wrong-footing Leno, and it was 1-1.

Before the second half, Guardiola gave a last exhortation to his charges in the tunnel and seconds into it, Kovacic scored again. Grealish passed to Foden on the left and he chipped to Silva, whose chest-and-pass to the Croat was as ruthless as the latter’s right-booted swish that beat Leno to the left.

Kovacic said: “It means a lot because my wife is pregnant so it was great to get some goals for the little one. It’s nice to score but the most important thing is the team and that we won today. Good game for us.”

Related: Pep Guardiola insists leaky Manchester City defence doesn’t worry him

On the hour a City double switch: Grealish and Manuel Akanji departed and Doku and Kyle Walker came on. Lewis, preferred in the XI instead of the captain, stayed at right-back, and Walker took Akanji’s central ­defensive berth. In balance, grace and technical mastery, Lewis is the blueprint Guardiola footballer: all of these characteristics were deployed in the thorax-control of the ball and volley that might have beaten Leno if not for striking Haaland.

Walker’s game centres on his renowned pace yet at 2-1 he could not stop Traoré speeding away before, once more, he lacked the lethal eye to beat Ederson. At the final whistle, he rued this and his other misses.