With Rodri serving the final game of his three-match ban, Kovacic joined Rico Lewis in the engine room at the Emirates, but his afternoon could very well have been cut short after just half an hour.
The Croatia international brought down Gunners captain Martin Odegaard with a shocking challenge on the Norwegian's ankle, which Michael Oliver punished with a yellow card while the VAR room decided whether the challenge warranted a sending-off.
Kovacic's challenge was akin to Malo Gusto's tackle on Lucas Digne and Curtis Jones's ankle-cruncher on Yves Bissouma, both of which saw the Chelsea and Liverpool men sent off after VAR reviews.
However, John Brooks and Darren Cann saw no need to upgrade Kovacic's sanction, but just a few minutes later, the former Chelsea man lunged in late on Declan Rice inside the Arsenal half.
Arsenal's incensed players and supporters justifiably called for Kovacic to receive a second yellow for challenge, but Oliver immediately waved away their appeals, much to the bewilderment of pundits.
Gary Neville stated that Kovacic was "very lucky" to still be on the pitch, a view shared by PGMOL chief Webb, who believes that Oliver did not want to 'overreact' by ejecting the 29-year-old.
Speaking to Michael Owen for Mic'd Up on Sky Sports News, Webb also expressed his opinion that the VAR would not have overturned Oliver's decision to send Kovacic off had he been given a straight red card for his tackle on Odegaard.
"This is clearly a poor tackle and I'm confident if a red card had been given by Michael Oliver on the day, it would have been a very straightforward "check complete", but he doesn't," Webb said.
"Second yellows are something the VAR is not able to get involved in. But he was extremely fortunate to stay on the field. (Oliver) doesn't want to have a negative impact on the game by overreacting to something.
"But it is also true that if you under-react you have a negative impact. He will realise the second one should have been a yellow card, which would have seen Kovacic sent off."
After his lucky escape, Kovacic was surprisingly sent out for the second half by Pep Guardiola, but he was eventually replaced by Matheus Nunes with 68 minutes gone.
Despite that sense of injustice, Arsenal did not need an extra man to subject Man City to back-to-back Premier League defeats, as Gabriel Martinelli came off the bench to net a deflected winner in the dying embers.
The Gunners remain unbeaten in the league this term and enter the international break second in the table, two points above the champions only behind arch-rivals Tottenham Hotspur on goals scored.
As well as the Kovacic incident, Webb also weighed in on Luis Diaz's disallowed goal during Liverpool's recent defeat to Tottenham, which saw the Colombian's effort wrongly ruled out due to a "significant human error".