22-year-old Brooksby from the USA went hard against the Norwegian, who after Nadal's exit from the tournament had to wear the favorite shirt.
The first set was won with 6–3, which was followed up with 7–5.
Brooksby even managed to shake off three match points in the third set, before the 24-year-old from Oslo woke up and via tiebreak extended the match.
But this was not the Norwegian's day at the Rod Laver Arena in Melbourne.
The fourth set was won 6–2 to Brooksby, and the Norwegian is thus eliminated.
Andrej Rublev is through to the third round after defeating Finland's Emil Ruusuvuori in the Australian Open.
The world number six from Russia connected early on and took a 2-0 lead in the set.
Certain blue and white top lit up after a tiebreak victory that reduced the set numbers to 2–1, but then Rublev won the fourth 6–3.
Ruusuvuori, ranked 46, admits he didn't have much to contend with.
- He came in hot, he played too fast, too hard.
I wasn't prepared for that, says the 23-year-old.
In what sense were you not prepared?
- It felt like the balls hadn't come that fast for a long time, I wasn't moving fast enough.
It felt like it was something I hadn't done in a long time, it took a little too long to get going.
But also the attitude, that I have to know that this is how they will play.