Zverev wins in latest-ever finish to a professional tennis match
Stay tuned with 24 News HD Android App
The Olympic champion saved two match points before completing a 3-6, 7-6 (12/10), 6-2 win at 4:54 am local time (1054 GMT).
The first-round tie at the ATP event lasted three hours and 19 minutes, the third match of Monday's schedule to pass the three-hour mark.
The previous latest finish was a 2008 Australian Open match between Lleyton Hewitt and Marcos Baghdatis that concluded at 4:34 am.
American Brooksby took the opening set but saw two match points come and go in the second-set tie-break.
Zverev eventually forced a decider on his fifth set point, winning a set that took 111 minutes.
Despite appearing to suffer from a cramp, the German world number three managed to find two breaks of serve in the third set.
Zverev will face his compatriot Peter Gojowczyk in the last 16.
Later Tuesday, Rafael Nadal will play for the first time since his record-breaking Australian Open triumph when he takes on Denis Kudla.
Daniil Medvedev, chasing Novak Djokovic's world number one spot, faces Benoit Paire.