At 16 years and 10 months, Fyvie beat David Goodwillie's record by more than a month with his first professional goal.
The midfielder opened the scoring at Tynecastle before second-half efforts from Darren Mackie and Derek Young wrapped up an easy win that moved the Dons to within a point of their opponents in the Scottish Premier League.
Hearts, meanwhile, started with an all-teenage strike force of Scott Robinson and Gordon Smith.
Smith replaced the suspended Christian Nade, while midfielder Ruben Palazuelos returned from a ban of his own.
Aberdeen welcomed back Lee Miller from a three-match ban, the striker ousting Paul Marshall.
Hearts were looking to extend their unbeaten SPL run to eight matches, their best sequence since George Burley led them to the top of the table more than four years ago.
The last time they went seven without defeat, Aberdeen were the side to halt their run, while the Dons also won the Active Nation Scottish Cup tie between the teams earlier this month.
Tonight's match was a meeting of the two sides with the worst disciplinary records in the SPL and it was certainly physical early on.
Ismael Bouzid suffered a facial injury that needed three minutes of treatment following a robust Darren Mackie challenge.
Marius Zaliukas teed himself up for the first shot on goal in the 10th minute, his effort drifting harmlessly wide.
The game was a real midfield battle and when Aberdeen won a skirmish two minutes later, they took the lead.
Mackie sent Fyvie clear and the teenager kept ice cool to stroke home.
Hearts tried to respond but they were looking lightweight up front, while their opponents continued to threaten on the break.
The hosts eventually began to get a grip on midfield and their fans were screaming for a penalty on the half-hour when Jerel Ifil bundled over Michael Stewart in the corner of the box.
Mike Tumilty waved play on, moments before Palazuelos' 20-yard left-footer sailed over the bar.
Hearts suffered a blow soon after when left-back Lee Wallace traipsed off to be replaced by Ian Black.
Seconds later, Richard Foster was booked for felling Stewart in full flight, the Hearts captain appealing for handball when his resulting free-kick hit the wall.
Black was making an impact, shooting over from long range and volleying tamely at Jamie Langfield four minutes before the interval.
Miller was forced to leave the field following an aerial challenge, while an off-balance Stewart steered a shot wide in first-half stoppage-time.
Mackie should have doubled the visitors' lead three minutes after the restart but he finished weakly from Foster's low cross.
But he made amends two minutes later when he stayed onside to beat the onrushing Marian Kello to a Mark Kerr flick and poked the ball past the goalkeeper.
A crucial challenge from Ifil prevented Zaliukas getting his shot away in the 55th minute before an Aberdeen breakaway almost killed the contest, Kerr's shot arcing just wide.
Hearts threw on David Witteveen for Smith, and Rocky Visconte for Palazuelos.
Seconds later, Mackie shot too close to Kello after racing clear again.
With 20 minutes left, Charlie Mulgrew was needlessly booked for chopping down Robinson on the touchline.
Mulgrew was quickly withdrawn for Zander Diamond, the injury-plagued defender's first appearance since the opening day of the season.
Aberdeen sealed the points with 15 minutes remaining when Young's flighted free-kick sailed straight in, Kello distracted by a number of jumpers.
Langfield smothered at the feet of Black as Hearts sought a consolation before Chris Maguire replaced Mackie.
Witteveen went down in the box under a challenge from Diamond, while Fyvie was withdrawn for debutant Nicky Low five minutes from time.
Kerr shot wide in the closing stages and Hearts' misery was complete when Black had to be carried off on a stretcher after suffering what looked a serious injury.