"Every day I have to push myself," Azarenka said. "It's not easy, even when it seems easy out there on court."
Azarenka will next play Begu, a Romanian who defeated Bethanie Mattek-Sands of the United States 6-4, 1-6, 6-2.
The match was interrupted in the second set for about 20 minutes after rainwater leaked from the roof onto the court.
The 57th-ranked Begu, who won her first career title in Tashkent last month, lost in qualifying but entered the main draw as a replacement for Anna Tatishvili of Georgia.
Goerges, who hasn't lost a set this tournament, beat Sofia Arvidsson of Sweden 6-1, 6-4. From 1-1 in the opening set, the German won seven straight games. Arvidsson broke back to tie it 4-4 in the second but then dropped her serve for the fourth time.