The Blues were on top in the first half, but the home side defended doggedly and went ahead after the break before Aymeric Laporte levelled with his first goal for the Club.
City created a couple of decent chances in the opening 15 minutes that both could have resulted in goals.
Raheem Sterling wriggled into the box and into the six-yard box but having done the hard work, his final pass was easily cut out by the Wolves defence.
Then a smart move that started with Benjamin Mendy’s clever ball to Sergio Aguero on the edge of the box and the Argentine’s cushioned header found the run of Ilkay Gundogan, but the German shot tamely at Rui Patricio.
Wolves, neat and tidy in possession, looked threatening when they attacked and the home fans thought their side had gone ahead when Jimenez tapped home at the far post on 20 minutes – but he’d strayed slightly offside and the goal was ruled out.
It stung City into a double riposte that stunned the home side as moments after Aguero turned a low drive onto the post and then Sterling hit a 25-yard screamer towards the top right-hand corner only for Rui Patricio to make a superb fingertip save onto the crossbar.
It was a half of almost in fact, entertaining, but ultimately goalless.
Wolves were organised and disciplined, making it difficult to find space between the lines and as the Blues continued probe, the home side broke forward and almost went ahead when Helder Costa broke forward and forced a fine save out of Ederson.
From the resulting corner, the hosts controversially went ahead when Joao Moutinho’s cross found the unmarked Willy Boly who bundled the ball home with his right arm – whether intentional or not, it almost certainly shouldn’t have stood.
City responded quickly and were denied a penalty by referee Martin Atkinson when David Silva appeared to be pushed over in the box.
It was a relief as it felt as this may be one of those days when nothing went in and with 20 minutes or so remaining, there was time to go on and find a winner.
Wolves went mightily close to a winner through Jota in the dying moments as he fizzed a shot a foot or so over the crossbar and then Aguero’s 25-yard free-kick struck the woodwork with virtually the last kick of the game.
By the time the final whistle blew, a draw seemed a fair enough result on a day when the champions were not quite at their purring best.
Wolves tactics spot-on? Or City out of luck?
Wolves defended in numbers and crucially, in the areas City generally hurt teams.
It was backs to the wall stuff from the hosts, who will cause problems to a number of teams on this evidence as they quickly make the transition to Premier League football.
Though it may feel like two points dropped, the Blues were tested in every department and the hosts will feel they thoroughly deserved something from the game.
Would VAR have given City more?
You could argue that the main decisions went against the Blues in an entertaining clash at Molineux.
The Wolves goal went in off Boly’s arm and Silva was denied a spot-kick that might have been given after a review.
That said, Wolves had a goal correctly chalked off in the first period.
Commanding presence in defence from the Frenchman and, on this occasion, attack, too.
“It was a good game for the spectators, but we conceded too many counter-attacks and missed simple passes.
“We created a lot of chances against a team who had ten men behind the ball which is a positive.
“We played a 5-4-1 and we didn’t create that many opportunities with that system last season, but today we did.
“It was a good point, but we hit the woodwork three times and their keeper made some very good saves as well. Sometimes they go in, sometimes they don’t.”
“We played the same level in the first four games this season as we did last season – it is hard to play against good teams who defend in numbers and counter-attack well, so, as I said, I was surprised how many opportunities we did create.
“We tried, created chances but sometimes the final ball wasn’t good, but we will improve because defensively we weren’t as solid as we normally are.
“We knew how good Wolves were last season and that they are strong with the players they have so we knew this would be a hard game already.
“Every game we play, we learn more and today is no different.”
City take on Newcastle United next Saturday at the Etihad, kick-off 5.30pm.