Substitutes Rickie Lambert and Steven Davis put a dogged Southampton side 2-1 in front and wipe out Carlos Tevez's opener for City.
But Samir Nasri spared City from an opening weekend upset by scoring an 80th-minute winner following Edin Dzeko's equalizer.
"We showed great character," Nasri told Sky Sports television. "We didn't panic."
Chelsea had no such troubles overcoming Wigan in Sunday's other match.
New signing Eden Hazard made an immediate impact, setting up Branislav Ivanovic's opener and winning the penalty from which Frank Lampard converted to clinch a 2-0 victory.
For City, the new season picked up where the last one ended for pulsating drama at Etihad Stadium. A 3-2 victory in May against Queens Park Rangers -- secured in the final seconds -- ended City's 44-year title drought.
"It was like the last game of the season, we've started the same and I hope at the end it will be the same result for us," Nasri said.
Although City didn't leave it until stoppage time on Sunday to produce the winner, manager Roberto Mancini hopes every game won't be as tough.
"It is important to have this character, it is better the next time to close the game," Mancini said. "We had too many chances to close the game -- we didn't."
City had to cope without Sergio Aguero from the 14th minute after last season's top scorer fell awkwardly following Nathaniel Clyne's challenge.
The Argentina striker went to hospital for a scan on his injured knee, but the results won't be known for another two days.
City's fortunes didn't improve after Aguero's injury. Even though Tevez won a penalty two minutes later, after falling to the ground under Jos Hooiveld's challenge, David Silva's tame spot kick was easily saved by Kelvin Davis.
Tevez found the target five minutes before halftime. He was fed through by Nasri and sneaked in front of Joe Fonte before sending the ball into the net at Davis' near post.
City squandered chances to extend its lead after the break, with Gael Clichy sweeping the ball over, and David Silva hitting the crossbar.
City was made to pay for those misses when Lambert, last season's top scorer in the second tier, scored his first topflight goal.
Four minutes after coming off the bench, Lambert seized on confusion in the City defense and Joleon Lescott's missed clearance to side-foot the ball past goalkeeper Joe Hart.
Another substitute also quickly delivered. Steven Davis had been on the pitch only three minutes when he buried the ball into the bottom corner of the net in the 68th after City debutant Jack Rodwell had lost possession to Southampton inside his own half.
But City recovered from its sloppiness, with Dzeko blasting in the equalizer four minutes later.
Nasri secured the three points after Southampton left back Danny Fox inadvertently headed the ball to the France midfielder, who was booked for lifting his jersey in the goal celebration to reveal a t-shirt with the "`Eid Mubarak" greeting to mark the end of Ramadan.
"We deserved to win the game," Mancini said. "They didn't have any chances in the first half and we had four or five incredible chances."
Chelsea made a surging start at Wigan following its tepid league campaign last year in which it finished sixth but made amends by winning the Champions League and FA Cup.
Roberto Di Matteo's side was in front after just two minutes, with Hazard turning Ivan Ramis and slipping the ball through for Ivanovic to race onto and dispatch into the Wigan net.
"(Hazard) was brilliant," Chelsea midfielder Frank Lampard said.
"It's a young age to come into the Premier League, no matter how good of a player you are."
Ramis was struggling to cope with Hazard and gave away a penalty when he fouled the Belgium international just five minutes after Ivanovic's opener.
Lampard scored from the spot, but the Blues couldn't build on the margin of the victory as Wigan finished with nothing to show for its domination.
"They took their chances really well, they punished us massively," Wigan manager Roberto Martinez said. "It couldn't have been a harder test ... I thought Chelsea were happy to defend well and run the clock down, and I took that as a real compliment to the side."
Manchester United's quest for a 20th title doesn't start until Monday, when former Arsenal striker Robin van Persie will hope to make his debut at Everton.
Everton's neighbor, Liverpool, was on the receiving end of the biggest shock of the opening weekend, with Brendan Rodgers' new side losing 3-0 at West Bromwich Albion on Saturday.