A repeat of last season's FA Cup final saw no sign of another upset as Edin Dzeko, Yaya Toure and Jesus Navas all joined the impressive Montenegrin on the score sheet.
The hosts squandered a number of good opportunities in the first 30 minutes as they looked determined to get their revenge for last season's FA Cup final defeat to the same opposition, before Edin Dzeko eventually got the breakthrough.
Jovetic doubled their lead in the second half before substitute Yaya Toure scored a delightful free kick, but there was still time for the Montenegrin and Jesus Navas to add the fourth and fifth.
Fresh off their 4-1 derby day demolition of Manchester United on Sunday, City boss Manuel Pellegrini made 10 changes, with Fernandinho the only player to keep his place. Seventeen-year-old Marcos Lopes made only his second appearance for the club, while Jovetic played his first game at the Etihad Stadium following a summer move from Fiorentina.
Wigan swept Ipswich Town aside with a 2-0 win Sunday and just the two players remained in the side for the short trip to Manchester, as Thomas Rogne and Leon Barnett started at the back.
The Premier League side was unsurprisingly in control from early on and they almost took a fifth-minute lead, but Lee Nicholls parried Dedryck Boyata's header wide following a James Milner corner.
City was producing plenty of crosses as Dzeko nodded a Milner centering feed wide before the England international emulated the Bosnian a few moments later following Lopes's delivery.
Lopes struck the crossbar with a superb effort just before the half-hour mark, but City did eventually take the lead in the 33rd minute as Dzeko made amends for his previous wasted efforts by looping a volley over Nicholls after Fernandinho's clever scooped pass.
Pellegrini had the luxury of being able to bring Toure on for Fernandinho at the break and City was no less dominant at the beginning of the second half, with Dzeko testing Nicholls once again in the 55th minute.
Five minutes later, City added to its lead. Nicholls thought that he had made a save from Jovetic initially, but the Montenegrin's effort after a Micah Richards cross struck the goalkeeper and went in.
If there was any doubt regarding a City win, Toure made sure that the side would go through to the next round 15 minutes from time as he fired an unstoppable free kick past Nicholls after Fraser Fyvie had fouled Jovetic.
City grabbed a fourth in the final 10 minutes as Jovetic poked past Nicholls following Milner's cross, and Navas got his first for the club with a low right-footed effort to complete the rout, latching onto Alvaro Negredo's through ball.