The 19-year-old - who had never scored a County Championship century before - came in at 96-3, hitting 15 sixes and 26 fours before he was dismissed for 234 off 136 balls.
Donald took just 123 balls to reach 200, equalling Ravi Shastri's record.
Derbyshire's young seamer Will Davis claimed a career-best 5-123.
The visitors did not help their cause with a series of missed chances.
Nick Selman made a second fifty in his first four Championship innings, while Will Bragg rode his luck for a patient 60.
But it was Donald who caught the eye, reaching 100, 150 and 200 with sixes as he took the Derbyshire spinners apart.
Glamorgan batsman Aneurin Donald told BBC Wales Sport: "I'm extremely pleased. It's nice to get the guys into a strong position first and foremost, but nice to hit them so well and come out with a big score. I've been looking for one and finally it came, although I rode my luck at times.
"It was a good wicket, the bowlers were getting a bit tired and it's a small ground, so it's about making the most of it. I knew the highest score was here [Glamorgan's record of 309 not out by Steve James] so obviously there's a good history.
"It's a good place to be [in the six-hitting zone], you don't get there too often, you end up not thinking about it too much and it flows.
"You don't get too many days like this and it was nice to make the most of it. I didn't know [about the fastest all-time double-century] until I walked off. I would have tried to get it a bit earlier."
Teenager Aneurin Donald equalled the record for the fastest first-class double-century as Glamorgan took charge of day one against Derbyshire.