City fell behind in the game when Willy Boly guided the ball into the back of the net for the hosts in the 57th minute with his hand but no officials saw it and the goal was given.
Aymeric Laporte, though, equalised for City 12 minutes later with a bullet header to seal a point for City in a game they will rue a number of missed chances in.
Wolves, though, will feel that this performance shows that they have finally arrived in the Premier League and will now look to push on against West Ham United next weekend as they look to secure their first win of the season.
The offside flag denied Wolves an early opener
As you would expect as the home side, Wolves started the game brightly by pressing the visitors high up the pitch and that almost resulted in them taking the lead in the 20th minute.
Vincent Kompany gave the ball away to Diogo Jota in a good position with the winger's cross finding Raúl Jiménez in the box with the forward putting the ball into the net only for the linesman to put his flag up for offside which was the right decision.
City struck the woodwark twice in a matter of minutes
That moment seemed to spark City into life as they hit the woodwork twice in a matter of minutes, showing their own intention to take the lead in the game.
Sergio Aguero was the first to hit the woodwork as his curling effort from just inside the box hit the post after a Kyle Walker cross and then Raheem Sterling unleashed a fantastic long-range strike which was heading into the top corner of the net only for Rui Patrício to touch the ball onto the crossbar.
City continued to pile on the pressure after that as the hosts started to drop deeper and deeper into their own box and but for some last-ditch defending from Boly on a couple of occasions, then the visitors would have taken the lead.
As the half came to a close, though, the hosts started to get more encouragement from the game as the City players started to give the ball away more, but it didn't lead to any chances as the half ended with the game goalless with the hosts the happier side at the break.
Nuno changed his tactics at the start of the second half
The start of the second half saw a change of tactics from Wolves as Nuno Espírito Santo set his side up to sit back and allow City to have the ball and hit them on the counter attack when they could.
This tactic caused City to become more frustrated and on the break, Wolves almost took the lead when Hélder Costa was played through on goal but he was denied by a good save from Ederson.
Controversial Boly goal gave Wolves the lead
From the resulting corner, though, Wolves did take the lead as Boly guided the ball home into the back of the net off his arm from a brilliant João Moutinho cross to give the hosts exactly what they had hoped for in the game.
Therefore, it was down to City to try and get themselves back in the game and they did just that 12 minutes after falling behind.
Laporte equalised for City with a bullet header
The goal was scored by Laporte as his bullet header from a İlkay Gündoğan free-kick flew into the back of net leaving Patricio with no chance in the Wolves net to equalise for the defending champions.
City looked refreshed after equalising and they almost turned the game around when a brilliant cross from Benjamin Mendy found second-half substitute Gabriel Jesus in the box but his header from close range was well-saved by Patricio.
Wolves held on for a draw despite Aguero hitting the bar late on
The visitors pushed and pushed to try and get the winning goal before the end as Wolves stood firm in defence but Aguero came within inches of scoring the winner from a free-kick in the last minute of injury time but the striker saw the ball hit the bar.
Not long after that free-kick, referee Martin Atkinson blew his whistle to end the game as both sides had to settle for a point in the game which both sides had chances to win.