Delap, who is the son of former Stoke City favourite Rory, was an unused substitute for City's opening 3-1 Premier League win at Wolves.
With Sergio Aguero sidelined due to a knee injury and Gabriel Jesus rested as the only remaining specialist striker in Guardiola's squad, the 17-year-old was handed a start at the Etihad Stadium on Friday (AEST).
He duly opened the scoring in the 18th minute, showing pace and power to latch on to Phil Foden's throughball and clip a brilliant left-footed finish into the top right corner.
Foden netted the winner 15 minutes from time after Sam Surridge found a quick response to Delap's strike.
Speaking at a post-match news conference, Guardiola pointed to the example of Foden, who also made his debut at 17 but had to be patient in his quest to become a first-team regular.
"We see in training how good a finisher he is," the City manager said of Delap. Now he has to be calm and keep working.
"We are delighted with his performance - he played really well.
"The situation that we have right now is we have just 13 players available in the first team. We need players from the academy, not just in training sessions.
"With the problems we have up front, Liam will stay with us. We'll use him but we cannot forget how we spoke about Phil in previous seasons."
Delap shone brightest in a youthful City line-up, that featured Eric Garcia and Taylor Harwood-Bellis at centre-back, Tommy Doyle in midfield and playmaker Adrian Bernabe at left-back.
The latter endured a miserable outing and left the field on a stretcher before half-time.
Afterwards, attention turned back towards Delap and Guardiola was keen to praise City's academy production line, which churns under the watchful eye of former England winger Jason Wilcox.
"He is just 17, he has a lot of things to improve. They need their own time, we cannot anticipate the process of each young player," he added.
"Congratulations to the academy for all the guys that are involved, scouting to recruit these players and all the managers in the academy.
"At the end I have the finished product, the last steps, but before there are a lot of players working for this. Jason Wilcox is now the boss in the academy who helps us to have these players."
Having stayed in contention for a fourth consecutive EFL Cup success, City host in-form Leicester City in the Premier League on Sunday.