Having not trailed in any of his first 10 matches as City boss, which had yielded a perfect 10 wins, Guardiola saw his side come from behind three times to earn a point in their Champions League Group C clash at a hostile Celtic Park.
The hosts went into the match looking to respond to their 7-0 defeat to Barcelona on matchday one, and they made a blistering start to the encounter by taking the lead inside three minutes through a controversial Moussa Dembele goal.
James Forrest latched on to a floated free kick before turning the ball back into the middle for Erik Sviatchenko, whose header bounced off the chest of an unwitting Dembele and in. Replays showed that the young striker was in an offside position, but the flag stayed down as he peeled away to celebrate Celtic's fastest ever Champions League goal.
The Hoops' free-scoring domestic form had been in sharp contrast to their European start, but they looked much more comfortable in their first home Champions League group game since 2013 and almost doubled their advantage moments after the opener when Claudio Bravo was forced into a smart reaction stop to deny former City defender Kolo Toure.
Celtic's intensity had City on the back foot in the opening stages, but they soon responded to being behind for the first time in the Guardiola era and levelled things up in the 11th minute when Fernandinho collected Aleksander Kolarov's scuffed effort before tucking his finish into the bottom corner.
The home side refused to relent despite the setback, though, and almost regained the lead just three minutes after the equaliser when Tom Rogic steered a low free kick narrowly past the post on the goalkeeper's side.
Brendan Rodgers's side wouldn't have to wait too much longer to restore their advantage, though, and the former Liverpool boss had one of his old proteges to thank as a sweeping move ended with Rogic threading a pass through to Kieran Tierney, whose resulting effort deflected off Raheem Sterling and past a helpless Bravo.
Sterling atoned for his error just eight minutes later to cap off a breathless opening half-hour, latching on to David Silva's through-ball before keeping his composure with a smart turn and sliding home for his fifth goal of the campaign. In doing so, Sterling became the first English player to score a goal and an own goal in the same Champions League game.
The England international almost turned into an unwitting provider shortly after the half-hour mark when Nicolas Otamendi reacted well to turn Sterling's sliced volley towards goal, but his header dropped narrowly wide as both sets of players stood watching.
The frenetic tempo of the game slowed somewhat towards the end of the first half, but Ilkay Gundogan almost sent the visitors into the break ahead when he curled a 20-yard strike just past the post.
The scores remained level going into the break, but parity did not last long after the restart as Celtic made an even quicker start to the second period than they had done in the first.
Again it was Dembele who did the damage for the home side, capitalising on Kolarov's error to hook an acrobatic overhead kick past a wrongfooted Bravo for his 13th goal of the season - all of which have come at home.
Nolito and Gundogan both drew routine stops from Craig Gordon as City went in search of yet another equaliser, and it was the former - in for the injured Kevin De Bruyne - who eventually got it when he tucked a rebound into an empty net after Sergio Aguero had been denied by the Celtic keeper.
City began to take control of possession as the second half wore on, and the hosts needed an important block from Sviatchenko to turn Aguero's firm header behind for a corner shortly past the hour mark.
The tempo of the game finally started to slow as Celtic began to retreat deeper and deeper, and Fernandinho almost stole the victory seven minutes from time when his 25-yard piledriver flashed inches over the crossbar.
City came close once again in stoppage time when Sterling teed the ball up for Gundogan, but this time Gordon came to his side's rescue with a fine reaction stop after the shot took a deflection on the way through.
Ultimately, though, Celtic held out for a memorable point in the first ever competitive meeting between the two sides, becoming the first side to prevent Guardiola's City team from winning this season.
The result means that Celtic move up to third in Group C on one point, while City remain second behind leaders Barcelona with four points from a possible six.