The Serbia international succeeded in securing a share of the points, on a night when the likes of Sergio Aguero, Samir Nasri, Edin Dzeko, David Silva and, late on, Carlos Tevez failed to score.
The equaliser was no less than City deserved having dominated throughout, hitting the woodwork twice, but the goal had seemed unlikely with the hosts looking like they had burned themselves out.
Napoli had probably anticipated they would be facing an attacking hailstorm at the Etihad Stadium and but for a couple of chances - Ezequiel Lavezzi hitting the crossbar for instance - they bided their time.
Their plans appeared to have worked when Edison Cavani, Serie A's leading goalscorer last season, snatched a classic counter-attacking goal.
But Kolarov, who has still to convince after more than a season at City, proved the unlikely hero.
Dzeko, with seven goals already this season, had looked a threat in the first half-hour but the closest he went to breaking the deadlock was when he exchanged passes with Aguero to fire a shot across goalkeeper Morgan de Sanctis and just wide of the far post.
Yaya Toure went even closer in the 35th minute. After sprinting 60 yards, having intercepted a corner on the edge of his own penalty area, the Ivory Coast international released Aguero in the inside-right position.
The Argentina striker ran into the penalty area, cut the ball back from the byline and Toure seemed destined to score only for the ball to hit the crossbar.
City had had a similar escape in the 18th minute when Vincent Kompany's slip allowed Lavezzi to advance into the box and curl a right-footed shot past Joe Hart but back off the woodwork.
But that was a brief sortie into enemy territory for the visitors as the direction of the traffic was almost entirely in the opposite direction.
The Italian side were under almost constant pressure, highlighted by the fact three of their back five were booked in the first half as they battled to keep out Mancini's marauders.
Kolarov's inswinging free-kick from wide on the right evaded everyone in the penalty area but not De Sanctis, who palmed it around the post.
Animated Napoli boss Walter Mazzarri spent most of the time on the touchline but could do little to organise his team into quelling the onslaught.
Despite enjoying the majority of possession City were given occasional reminders that at this level no team can be underestimated.
Just after half-time they were indebted to Kompany's goalline clearance for preventing Marek Hamsik's far-post cushioned volley under Hart producing the opening goal.
And after seeing wave after wave of attacks founder on a tough Napoli defence, City started to run out of ideas with 25 minutes to go.
The canny Italian side had waited patiently for this opportunity and in the 69th minute they seized it with clinical precision, having seen Hamsik denied a genuine goalscoring chance by the sliding Pablo Zabaleta.
Gareth Barry lost possession 10 yards outside the Napoli penalty area and left wing-back Christian Maggio raced 50 yards downfield to put Cavani through on the right of the box, and he slid a shot under Hart.
City's response was instantaneous with Aguero sidefooting Samir Nasri's near-post cross against the crossbar as a prelude to the equaliser.
In a side brimming with attacking options Kolarov showed them all how it should be done.
His 75th-minute free-kick from the right of the area dipped over the wall and crept in at the near post, much to the annoyance of De Sanctis.
It was the Serbian's last - and most important - touch of a night in which he also broke his nose, as he was immediately replaced by Gael Clichy.
Dzeko pushed his shot on the turn wide from 12 yards before he too made way for Tevez for the final 10 minutes but even the talismanic Argentinian could not produce a winner.
As a starting point on their return to Europe's elite after a 43-year absence it was not too bad for City.
They will come up against sides less happy to defend for lengthy periods in the shape of Bayern Munich and Villarreal in Group A and Mancini's side have already shown they have too much firepower to be denied for too long.