Gauff, Medvedev through in Australia as Djokovic begins record Slam quest
A bumper day two at the season-opening Grand Slam also sees six-time major winner Iga Swiatek, home hope Alex de Minaur and fourth seed Amanda Anisimova enter the fray.
But the tournament is over for seventh seed Felix Auger-Aliassime who retired from his opening match with cramp.
Gauff came through against Uzbekistan's Kamilla Rakhimova on centre court 6-2, 6-3, but was less than convincing, with seven double faults and 31 unforced errors.
"I tried not to put too much pressure on myself," she said.