Pep Guardiola’s introduction of Raheem Sterling after the break transformed this second group-stage match for Manchester City. Until then Dinamo Zagreb had stymied England’s champions, yet 10 minutes after entering Sterling had a 10th goal in 12 appearances and City were cruising to a second victory and had Group C in their control.

The forward completed a scintillating cameo by creating Phil Foden’s second on 95 minutes.

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“He’s a player who is always there, he has this talent,” Guardiola said of Sterling. “He loves to score goals, you always have that feeling. He said a few days ago he missed chances at Everton [where he also scored] but he was always thinking of the next one. I think still he can improve his finishing. Today the pass for Phil was perfect. But still there is a gap to be even more clinical – but it’s important that all the time he’s there and that’s why he’s been able to score the goals.”

Guardiola made five changes from the victory at Everton. Kevin De Bruyne was omitted due to a groin problem – his availability for the visit of Wolves on Sunday is in the balance – while Bernardo and David Silva, Benjamin Mendy, João Cancelo and Sergio Agüero all came in. Sterling, Gabriel Jesus, Oleksandr Zinchenko and Kyle Walker were the others to drop out.

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Zagreb had won their previous match 4-0 on Friday and arrived hoping to end a dismal streak of 12 consecutive losses in Champions League away group games. Guardiola’s wish that City fans be “seduced” by the competition was not answered during the pre-game anthem, which was booed as has become customary at the Etihad, and the contest was stopped almost instantly following kick-off when Rodri fell awkwardly. This may have affected City’s rhythm because they were slow to settle, with one needlessly loose pass from Agüero indicative of the wider problem.

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Guardiola had again plumped for the centre-back pairing of Fernandinho and Nicolás Otamendi but neither they nor the rest of the defence could stop Dino Peric rising to head at Ederson’s goal from a free-kick. The effort went too high.

Yet action in the visitors’ area was served up on a near-permanent loop until half-time, Agüero repeatedly receiving the ball and looking to fire a shot off or find Riyad Mahrez.

What kept the score level was a dogged Dinamo rearguard and the referee’s refusal to award a penalty when Kévin Théophile-Catherine seemed to handball near goal. The latter incident was surely an example of what VAR is supposed to clear up but Nenad Bjelica’s team were allowed to escape. Seconds later, David Silva also thought he had a decent penalty shout but Serdar Gözübüyük was again not interested in awarding the kick. By the interval, City had somehow failed to breach Dominik Livakovic’s goal though Guardiola’s instructions may have been to simply keep on keeping on, given his team’s dominance.

Facebook Twitter Pinterest David Silva goes to ground, but Manchester City were not awarded a penalty. Photograph: Robbie Stephenson/JMP/Rex/Shutterstock

What the manager will not have suggested was for Rodri to begin the second half by giving the ball up for Bruno Petkovic to run clear towards Ederson. But as his teammates waited to be played in the No 9 dawdled and the danger fizzled out.

Zagreb soon committed their own howler, a mix-up between Peric and Livakovic letting the ball spill to Agüero, who could not quite capitalise as the angle tightened. Next, a slick City corner ended with Ilkay Gündogan chipping the ball to the back post towards a lurking Agüero before Livakovic cleared with a punch.

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Eleven minutes into the second period Guardiola had seen enough, and he took off the muted Bernardo Silva for Sterling in an attempt to find the killer touch that had been absent. City camped in the final third but frustration grew as the yellow wall put up by Croatia’s champions remained firm. That was until, at last, the hosts made the breakthrough when Sterling hammered home a precise Mahrez cross and Guardiola celebrated with the home support.

The manager’s decision to bring on Sterling had gained City the ascendancy they deserved. What they did not receive was a penalty when Petar Stojanovic took Sterling down – but the decision looked correct, Stojanovic connecting with ball first. It did however spark a Guardiola tantrum and the Catalan was booked – much to his chagrin. This, though, ended as a satisfying evening for him and his side, capped when Sterling broke clear to set up Foden, the midfielder slotting coolly home in the closing moments.

Of the 19-year-old, who has never been selected for a senior England squad, Sterling said: “I am buzzing for Phil and I want him in the national team, if he keeps going he will be there.” It is indicative of City’s depth that Foden is not yet a regular in their XI.