Orient threatened to pull off a famous upset when it led 1-0 at halftime against Guardiola’s four-time defending Premier League champion.
It took goals from substitutes Abdukodir Khusanov and Kevin De Bruyne to secure victory for City at Brisbane Road.
“It was impossible to control,” Guardiola said. ”We played with character, and we are in the next round and it’s always nice.”
Orient went ahead in spectacular fashion when Jamie Donley’s shot from just past the halfway line hit the bar and rebounded off the back of City goalkeeper Stefan Ortega in the 16th minute.
It was officially credited as an own-goal, but Donley took the congratulations as he celebrated wildly in front of the home fans. He was also rewarded with the player-of-the-match award.
But the goal wasn’t enough to hold off City’s fightback.
Rico Lewis’ effort deflected off Khusanov in the 56th to level the match and De Bruyne flicked a shot past Josh Keeley in the 79th to seal victory.
It wasn't all good news for Guardiola, however, with $61.8 million midfielder Nico Gonzalez injured and substituted after 22 minutes of his debut.
More cup joy for Newcastle
Already in the final of the English League Cup, Newcastle advanced in the FA Cup with a 3-2 win against Birmingham.
But, like Man City, it was another case of a top flight team being pushed to the limit by third-tier opposition.
League One leader Birmingham, which is part-owned by NFL great Tom Brady, took the lead inside a minute at St. Andrew's through Ethan Laird. A stunning long-range goal from Birmingham's Tomoki Iwata pulled the game back to 2-2 before halftime.
Newcastle had to wait until the 82nd to regain the advantage when Joe Willock scored his second of the game. Callum Wilson was also on target for the visitors.
Bournemouth run continues
Flying high in the Premier League, Bournemouth is also through to the fifth round of the cup after a 2-0 victory over Everton.
Antoine Semenyo’s penalty and a goal for Daniel Jebbison put Bournemouth on course for the next round by halftime at Goodison Park.
Everton hit the post three times in the second half as David Moyes’ team mounted a fightback, but couldn’t find a way through.
Ipswich’s priority is to avoid relegation from the top flight this season, but a 4-1 win at second-tier Coventry kept its cup run going, with Jack Clarke scoring twice.
Southampton, last in the Premier League, lost 1-0 at home to a Burnley team that is fighting for promotion to the top division.
The latest shutout from Burnley was its 10th in its last 11 games.
Muniz double
Rodrigo Muniz scored both goals for Fulham in a 2-1 win at Wigan.
Wigan won the competition back in 2013 - beating Manchester City in the final - and was relegated days later. It has been out of the Premier League ever since and is currently in the third tier.
But it pushed top-flight Fulham, with Jonny Smith leveling the game in the second half before Muniz scored the second of his goals to seal the win.
Leeds, top of the second tier, was knocked out by Millwall — losing 2-0 at home.
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James Robson is at https://twitter.com/jamesalanrobson
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