Fellow teenager Tommy Doyle also gained valuable further first team experience, coming on as a second half substitute.
And reflecting on the win, the central defender said it was another vital part of the youngsters' overall education.
"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."
It was an especially memorable occasion for Harwood-Bellis, as he netted his first senior goal, with a deflected effort off John Stones’ second half shot, with the effort being allowed to stand after a lengthy VAR check for offside.
And Harwood-Bellis revealed it was a proud moment for both him and his family who were watching from the stands.
“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!”
Harwood-Bellis, who made his City debut earlier this season in our Carabao Cup win away at Preston, also admitted it was a special thrill to savour first hand the magic of the FA Cup.
“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."