The reigning champions were forced to dig deep to rescue a point on a day of mild controversy at Molineux, with Laporte's header in the 69th minute canceling out Willy Boly's opener 12 minutes earlier that went in off his arm.
It appeared Wolves might inflict a first league defeat on the Premier League champions since City's derby defeat to Manchester United in April.
The home side exposed some chinks in City's armor that will offer a glimmer of encouragement to the rest of the Premier League.
Nuno Espirito Santo's men weathered intense City pressure before claiming a surprise lead.
And even though City shared the points thanks to an emphatic header by Laporte, the game threw up rare questions for Guardiola to answer.
Having stormed to the Premier League title last season and started the new campaign in impressive style, life has been plain sailing for much of the past 18 months for Guardiola.
In the absence of the injured Kevin De Bruyne, however, the composure his side so often display in attacking areas was sometimes missing at Molineux, although they still created enough chances to see off Wolves comfortably.
Of more concern, perhaps, was the lack of solidity in defense, where Vincent Kompany and Laporte at its heart looked far from assured as a partnership.
With John Stones left on the substitutes' bench, there were signs that Kompany's lack of pace and Laporte's lack of experience could be exposed, although the young Frenchman looked like a seasoned Premier League campaigner when he thundered home the header to give his side a point.
Patricio save
A first half in which Wolves played their part in an entertaining spectacle was still, inevitably, dominated by the reigning champions, who struck the woodwork twice, once with the aid of a fabulous save from Rui Patricio.
The Wolves and Portugal number one threw himself high to his left to claw a long-range effort from Raheem Sterling onto the crossbar on 22 minutes.
That came shortly after Sergio Aguero had struck Patricio's left-hand upright with a snap-shot from a Kyle Walker cross.
That effort came from a break that followed a disallowed goal for Wolves, who had Raul Jimenez flagged offside after he had tapped home a cross-shot by Diogo Jota.
Fernandinho fired narrowly wide for City and Ruben Neves did likewise for Wolves, with Boly making two fine challenges on Aguero as the opening 45 minutes failed to produce a goal.
It was unusual territory for City, who then conceded a 57th-minute goal to add to their frustrations.
Joao Moutinho's delicious cross from the left skimmed the head of Matt Doherty and found Boly, with the ball finding its way into the bottom corner via his arm.
City believed the opener might have been ruled out for either offside or handball and they were further agitated when David Silva was denied a penalty for what he felt was a shove by Doherty.
But they were right back in the game when Ilkay Gundogan delivered a free-kick from the right and Laporte leaped above Boly to head home the equalizer from six yards.
Had a stoppage-time free-kick from Aguero dipped under the crossbar instead of striking it, City would have forgotten their frustrations.
