Clayton, 17, was on target just 10 minutes after coming on as a substitute to help Crewe to a 2-2 draw at Southend and a 3-2 aggregate victory.
Southend topped the table for much of the season while Crewe were languishing in 18th when manager Steve Davis took over in November.
But Davis' faith in the club's youngsters was rewarded when they sneaked into the play-offs on the final day and they will now face the winners of Thursday's meeting between Torquay and Cheltenham for a place in League One.
"It was the best feeling in the world to score, I was pleased to come on and it shows how good the academy is," Clayton told Sky Sports.
"I think we have got a great chance. We've got a great squad, we're in form, we've come late and I wouldn't fancy us not to win."
Man-of-the match Ashley Westwood added: "We were looking at a relegation battle but the gaffer has come in and changed it around and the players have got to take a lot of credit as well."
Ajay Leitch-Smith opened the scoring for Crewe and Neil Harris levelled on the night before Clayton struck with a well-taken goal on the counter-attack.
Shrimpers skipper Chris Barker pulled another back with three minutes remaining to ensure a nervy finish but they could not take the tie to extra-time.
Barker said: "We didn't turn up in the first half. In the second half I thought we were fantastic but we can't give a two-goal start to a team like Crewe, they're a good passing team but also work very hard as well.
"Eight months of the season have been good, we have been in the top five consistently and also at the top for quite a while but it doesn't count.
"It's going to be horrible watching the final next week."