Opponent Mikhail Kukushkin led 6-5 in the first set.
The sunny, hot and humid conditions at the Miami Open began to break down the wildcard that made its first match on the tour.
Draper looked noticeably affected and had his heart rate checked by medical staff before continuing the match.
The sun was shining in 28 degree heat.
- I started to feel my body a bit. I said I would continue because I did not feel faint.
When the young Briton returned to play and was about to hit back a set ball, he instead collapsed. He received an ice pack in the neck and interrupted the match.
- On the last ball, I did not collapse. I stumbled because I started to feel really dizzy and stuff. In the last few hours, I have been treated by physios, trying to recover as much as I can and looking ahead, he says.