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.
|VIEW FROM ETIHAD STADIUM
|By Tom Marshall-Bailey
Manchester City's 5-0 rout of Wigan may not be enough just yet to convince any doubters that remain about this side's capabilities on all fronts this year but the old adage that you 'beat what's in front of you' could not have been more apt this evening as the hosts did so in some style, thanks mainly to the magnificent Stevan Jovetic.
The Montengrin was first to every ball and notched his first two goals for the club to cap a promising home debut.
Edin Dzeko had already got the ball rolling and further sumptuous strikes from Yaya Toure's free kick and Jesus Navas's rifled near-post finish provided the perfect tonic for Manuel Pellegrini, who has seen his side strike nine times in two games.
City did not ever look likely to give Wigan a sniff of an upset, ruthlessly disposing of their FA Cup final tormentors.
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 on 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 were 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 were producing plenty of crosses as Dzeko nodded a Milner centre 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 were 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 their 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 they 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.