Brown, a qualifier ranked 189th in the world, had only once won a main-draw match at a grand slam before this week but produced a fine display of power and touch to win 6-4 6-4 6-7 (3/7) 6-2.
The 28-year-old is far from your average tennis player. With long, flowing dreadlocks and an unorthodox serve-volley game, he certainly stands out.
He has plenty of weapons, too, with a booming serve and forehand that caused Hewitt no end of problems.
Brown is far from all power, though, producing excellent drop shots and volleys, none better than the diving forehand volley that clipped off the top of the net and gave him the first set.
Brown leaped into the air as if he had won the tournament, but there was better to come.
Hewitt broke serve in the first game of the second set but Brown hit back to level at 2-2 and then broke in the 10th game as he had in the first set, pumping his fist into his chest as he bounced back to his seat.
The Australian always has great support, the ever-present Fanatics leading the way, and it looked like he could turn the match round when he came from 3-1 down to win the third-set tie-break.
But Brown was not finished and dominated the third set before leaving the court in tears as his achievement overwhelmed him.
Born in Germany but raised in Jamaica, Brown switched nationality in 2010 after becoming disillusioned with the lack of support from the Jamaican Tennis Association, picking Germany over Great Britain, for whom he qualified through his grandparents.
He used to tour European events in a camper-van, and admitted he could not quite believe the result, telling the BBC: "It's going to take a while to sink in.
"I'm not normally the type of guy to cry, I don't know what happened. I'm playing Lleyton Hewitt, a guy you're watching when you're growing up.
"I've won a lot of matches already playing qualies and a very good first round and that really helped me with my confidence to go into the match believing I could do it.
"Doing it and thinking you can do it are two things. I've been so often close to winning top matches and couldn't put it together. I've got to take a look at that (fourth) set on tape."