At 16 years and 10 months, he beat the previous SPL record held by David Goodwillie by more than a month.
Dons boss Mark McGhee said: "That's fantastic. What a good goal; what a finish.
"He had one earlier in the season when he might have gone through and scored and he didn't score.
"When I saw that tonight, I was just hoping he would go one better, so fantastic.
"That's why he's in the team, because he's got all these ingredients.
"You see him sometimes holding off men and then of course his running and now his finishing."
Aberdeen have been trying for some time to extend Fyvie's contract.
"All we're trying to do is prolong it and give him more money," McGhee added.
"At the moment, he's playing for almost youth-team money.
"We'd like to obviously fix that."