The Montenegro striker made his first City start in the Audi Cup clash in Munich following his £22m arrival from Fiorentina.
And he looked sharp as Manuel Pellegrini’s side raced into a 5-0 lead at the Allianz Arena inside 35 minutes.
Jovetic, 23, came off at half-time as he eased himself into pre-season, but has promised fans he will be fully up to speed by August 19 when City open their Premier League campaign at home to Newcastle.
He said: “It was my first game in pre-season and I am satisfied with the way I played.
“Before this I was just training on my own but I still feel good.
“I now have three weeks until the beginning of the Premier League and when I came off at half-time the boss said, ‘Well done’.
Edin Dzeko then took centre stage with a rapid double as City stormed into a five-goal lead.
But a crazy first half was not complete and Milan then scored three in six minutes, two from Stephan El Shaarawy and another by Andrea Petagna before the break.
Perhaps predictably there were no further goals in the second half as both sides made a raft of substitutions.
But Jovetic was delighted with such a sparkling performance from City.
He added: “We played very well and scored five goals in the first 30 minutes, which is a very good thing.
“I think we could have scored some more but then Milan came back, so in the end it was a good game.”