Slack defending from Reds debutant Alberto Moreno let Jovetic in just before the break at the Etihad Stadium on Monday night, the Montenegro international striker smashing the ball under Simon Mignolet after dispossessing Moreno as he dwelled on the ball.
Then after the interval, Jovetic added his and City's second, starting and finishing the move from close range.
Sergio Aguero then added a third a matter of seconds after coming off the bench, latching onto a pinpoint pass from fellow substitute Jesus Navas to make sure of the three points.
Pablo Zabaleta put through his own goal late on, but it was a mere consolation for the visitors.
It was all about City making a statement at the Etihad, and the manner of their emphatic victory certainly sent their title rivals a message.
The first 30 minutes was very cagey, as both teams played some good football without finding a killer pass.
Daniel Sturridge did come close to breaking the deadlock but after beating Vincent Kompany, the England forward fired straight at Joe Hart.
The deadlock was broken four minutes before the break. Samir Nasri clipped the ball into the box, it was half-cleared, but as Moreno dallied on the loose ball, Jovetic nipped in, stole the ball off Moreno's toe and smashed City into a half-time lead.
After the break, City got into their stride quickly, but Liverpool did have the ball in the net, only for Sturridge to be ruled offside.
Edin Dzeko should have done better after being put through, and was soon replaced by Aguero, who made the ultimate impact off the bench.
With his first touch, the Argentina striker ran onto Navas’ sublime pass, which was perfectly weighted for Aguero to take in his stride and slot the ball past a stranded Mignolet.
Liverpool did get themselves back into it. Sturridge’s cross was met by the head of substitute Rickie Lambert, whose effort was brilliantly saved by Hart, but Pablo Zabaleta inadvertently put the ball into his own net when trying to clear.
Lambert was again in the clear after a fortunate ricochet, but he elected to pass when he maybe should have been more selfish.
Liverpool finished the match with 10 men as Glen Johnson had to go off with an injury, with Brendan Rodgers having already used all his subs.
While not at their blistering best, City were clinical when it really mattered, and in Jovetic, they may have another player who can make a real difference in the title race.
The champions - who rise to third - host Stoke in their next assignment on Saturday, while ninth-placed Liverpool go to Tottenham in the Premier League on Sunday.