The defending champions - who had quickly reassumed their place at the top of the table courtesy of a 6-1 win over Huddersfield Town last time out - came closest to breaking the deadlock in the first half when Sergio Aguero and Raheem Sterling both hit the woodwork within a minute of each other.
However, Wolves held their own and took the lead shortly before the hour mark - albeit in controversial circumstances as Willy Boly's final touch came off his hand before bobbling into the bottom corner.
City hit back through a thumping Aymeric Laporte header 12 minutes later and almost made it three wins from three with the final meaningful action of the match when Aguero crashed a free kick against the crossbar.
Wolves survived to claim a second successive home draw upon their return to the Premier League, although they are still searching for their first top-flight victory since February 2012.
Wolves boss Nuno Espirito Santo insisted before the game that his side would not alter their attacking style for the visit of the champions, and his unchanged XI held their own for the opening 20 minutes as the match showed encouraging signs of living up to its billing.
City's best moments in those early stages came down the left channel, with one such attack seeing Aguero cushion a header into the path of Ilkay Gundogan, whose tame effort was denied at the near post by Rui Patricio.
Wolves' only sight of goal in that time came from range when Ruben Neves fired well off target, but they momentarily appeared to be rewarded for their positive attitude when they had the ball in the back of the net after 20 minutes.
A mistake from Vincent Kompany left Wolves with a two-on-one situation and Diogo Jota's eventual shot deflected into the path of Raul Jimenez, who tucked home a simple finish from close range but was greeted by the unwelcome sight of the offside flag when wheeling away to celebrate.
It was a significant scare for the visitors, but it seemed to spark them into life and just 30 seconds later Aguero latched on to a deflected low cross into the box before thumping a first-time effort against the foot of the post.
Patricio was beaten on that occasion, but the Portugal international needed to be at his very best less than a minute later as City stepped up the pace.
Sterling engineered room to shoot and unleashed a brilliant swerving half-volley which looked destined for the top corner until Patricio matched it with an early save-of-the-season contender, clawing the ball against the crossbar with a stunning one-handed stop.
City's pressure was relentless during a 10-minute spell midway through the first half, though, and it took a fine last-ditch challenge from Boly to deny Aguero a clear chance shortly before the half-hour mark.
Fernandinho was the next to come close when he dragged a low strike narrowly wide of the target, but Wolves weathered the storm and soon began to grow back into the game, with Neves flashing another effort off target from range.
The home side's best chance of the first half arrived shortly afterwards when Jimenez brought the ball down inside the box and worked space to shoot, only to slice his half-volley closer to the corner flag than goal from a tight angle.
Benjamin Mendy's performance was not as influential as it had been in the opening two games of the season, but he did almost conjure up a chance towards the end of the first half when his vicious cross was only palmed into the path of Aguero, who could not sort his feet in time to truly test Patricio from the follow-up.
Wolves will have been happy with their first-half performance as they took City into the break still goalless, and while Pep Guardiola's side controlled the early stages of the second period too, the best chance they could conjure saw Kompany head over from a Gundogan corner.
Indeed, the breakthrough came courtesy of Wolves, but not before they had given City a warning shot moments earlier when Helder Costa broke down the left flank and saw his powerful effort well saved by Ederson at the near post.
The resulting corner saw Joao Moutinho exchange a one-two with Neves before swinging a delightful cross into the box which Boly bundled home at the back post - although replays showed that the final touch came off the defender's arm.
There were surprisingly few complaints from City's players as a new debate over VAR began to brew, with Guardiola's side instantly turning their attention to getting back into the game. David Silva saw one shot blocked moments after falling behind and then felt as though he should have had a penalty for a trip by Neves inside the box.
Gundogan then drew a routine stop from Patricio, but true to Nuno's pre-match promise Wolves refused to retreat into their shell and still posed problems on the counter-attack. Indeed, Neves should have done better when he drilled wide from the edge of the area after 66 minutes.
City's equaliser came just three minutes later as Gundogan clipped a free kick into the box which Laporte attacked with gusto, thumping his header past a helpless Patricio for his first ever Premier League goal.
The smart money at that stage would have been on a City victory, with Aguero seeing another penalty shout turned down before firing wide, and Gabriel Jesus squandering a golden chance when his close-range header was straight at Patricio, who still had to make a smart save.
Wolves had the threat of club-record signing Adama Traore on the break, though, and the home debutant almost inspired Nuno's side to victory with two minutes remaining of normal time by skipping past two defenders and standing the ball up into the middle for Jota to take down on his chest and fire narrowly over the crossbar.
Moments later Traore once again left Mendy for dead down the flank before drilling a dangerous cross into the box, but this time Kompany was well-placed to deny Jimenez a tap-in.
The pace of the substitute provided welcome relief for Wolves, but all of their hard work was almost undone by a moment of genius in the fifth and final minute of stoppage time when Aguero fired a free kick towards goal, only to be denied by the woodwork once again.
The result leaves Wolves now winless in a club-record 17 top-flight matches and 14 in a row at home, but Nuno will have been encouraged by another promising performance for his side despite their wait for victory extending three games into the new season.
Man City, meanwhile, see a seven-match away winless streak come to an end and could surrender top spot in the day's later games, with Liverpool in pole position to take advantage of this slip-up when they host Brighton & Hove Albion in the evening kickoff.
WOLVES (3-4-3): Patricio; Bennett, Coady, Boly; Doherty, Moutinho, Neves, Castro (Vinagre 85'); Costa (Traore 72'), Jimenez, Jota
MAN CITY (4-3-3): Ederson; Walker, Kompany, Laporte, Mendy; Silva, Fernandinho, Gundogan (Sane 77'); Bernardo (Jesus 62'), Aguero, Sterling (Mahrez 85')