Oleks Zinchenko gave City the lead midway through the first-half, only to be leveled back just 15 minutes later.
But Sergio Aguero, Taylor Harwood-Bellis and Phil Foden all scored to ensure passage into the fourth round. It was Harwood’s first start at home and he pointed it with a goal.
A win and to next round we go.
On to the reaction-
Pep Guardiola Reaction
“We are in the next round after an incredible amount of games,” said Pep.
“We played seriously. In the first half we struggled a bit, but the second half was better. I think in general the team did okay.
“Our game was there all the time. In the Premier League we are far away, we have to focus on taking second position. In the other comps we go game by game.”
“Taylor, when he’s played this season, he’s played really well.
“Of course, he’s young and now he’s already scored for Manchester City - it was a bit of a weird goal, but it’s a goal. It’s important he plays at a good level. Eric Garcia and Taylor are young, but they play more than well.
“Young players have to not talk too much, listen and learn.
“They have to learn. The future is in their hands. The privilege for us has to be in this club and play minutes with this team.”
“Tommy played in the Carabao Cup and played a few minutes today. It’s not because they are English, it’s because they are good players.
“We don’t give presents. What we have seen so far, they have the quality to help us.”
“Yep, I agree,” he said. “The opponent team when it’s not a goal, celebrate that. It’s weird.
“Every time it’s a goal, you have to wait on the behaviour of the ref.
“When it’s clear, like the fourth goal you can celebrate. The other ones you have to wait. We have many experiences of that..
“There are many situations when it’s not clear.”
“I saw their manager and the sporting director. It’s nice for us to host these clubs and for their players to realise we are the same.
“We are a different level, but dreams are dreams.”
“We are just doing all we can to show the manager that we are capable of playing,” said Harwood-Bellis.
“When we do get the chance, we want to try and take it.”
“I’ll take the goal. There was a bit of luck with it coming off John’s shot but I’ll take it,” Taylor added.
“It was quite obvious it came off me.
“When went it to VAR I thought I could be offside but fortunately it was OK.
“I’m not there to score goals but I found out I wasn’t (offside) and I’ll take it... a goal is a goal!”
“It’s a competition I have been watching since I was a boy and to play in front of the home fans for the first time was a great occasion for my whole family,” he added.
”They [Port Vale] did OK to start off with but we have enough quality in our team to react and bounce back and score a couple of goals like we did.”