Azarenka suffered with illness throughout her match against 14th seed Roberta Vinci but dug deep to win 6-4 6-2.
Trailing 4-3 in the opening set, having let a break of serve slip away, Azarenka received medical attention at courtside including a blood pressure test.
She returned to win the next three games, and with them the first set, despite still looking in some discomfort.
A break in the opening game of the second, her fourth game in succession, suggested the stricken Belarusian was in a hurry to finish the contest and a second left Vinci seeking advice from her coach at the change of ends.
The run ended at seven straight games and Vinci then broke to trail 4-2, taking her third break point with a defensive lob after Azarenka failed to put away an overhead.
But the favourite immediately broke again and saved two more break points herself to win the match.
Caroline Wozniacki, now down at 10th in the seedings, won her high-profile clash with Li Na in three sets.
The seventh-seeded Chinese took the opener but Wozniacki battled back to win 4-6 6-3 6-4 in two-and-a-half hours.
Urszula Radwanska and Petra Martic were unable to follow up their upset wins on Tuesday as both were eliminated in contrasting fashion.
Croatian Martic, who on Tuesday beat fourth seed and 2011 Wimbledon champion Petra Kvitova, pushed 17th seed Nadia Petrova all the way before losing 7-6 (7/2) 6-7 (1/7) 6-4 in three hours and 10 minutes.
But Radwanska, the conqueror of Ana Ivanovic, was hammered 6-1 6-1 on Wednesday by fifth seed Angelique Kerber inside 48 minutes.
Her third-seeded sister Agnieszka, who also eliminated a former world number one on Tuesday in the form of Jelena Jankovic, marched on with a 6-4 6-3 win over American qualifier Jamie Hampton.
Maria Sharapova, seeded second, eased past Czech Lucie Safarova 6-2 7-6 (7/5) in a match featuring 12 breaks of serve, seven of them to the Russian, in only 20 games.
Italian Sara Errani came from behind to beat Marion Bartoli of France 3-6 6-2 6-2 in a match which pitted the sixth and ninth seeds against each other.
Eighth seed Sam Stosur was not unduly tested as she saw off Dominika Cibulkova, seeded 12th, 6-4 7-5.