The American, 32, controlled her contest against 31st seed Daniela Hantuchova to win 6-3 6-3, a tournament-record 61st singles victory.
Fourth seed Li Na, runner-up in 2011 and 2013, survived a huge scare to edge past Lucie Safarova 1-6 7-6 (7-2) 6-3
Third seed David Ferrer beat 29th seed Jeremy Chardy in straight sets.
The conditions continued to be an issue for players, with the temperature reaching a high of 41.4C a day after matches were suspended because of 43.3C heat,
also see ( Schumacher may never wake-up from coma)
Rod Laver Arena
S Williams (US) [1] beat Hantuchova (Svk) [31] 6-3 6-3Five-time champion Williams was not at her best and appeared to be struggling with the heat, though she still proved too strong for Hantuchova.
The world number one raced into a 5-3 lead but had to save two break points to hold serve before clinching the first set.
Williams, who has yet to drop a set in the tournament, broke early in the second but her opponent was in battling mood and responded to level at 3-3.
also see ( Schumacher may never wake-up from coma)