Serena Williams of the US reacts after winning a point against Garbine Muguruza of Spain during their women's singles fourth round match at the Australian Open 2015 tennis tournament in Melbourne January 26, 2015. [Photo/Agencies]

MELBOURNE - Serena Williams avenged her heaviest Grand Slam defeat with a comeback 2-6, 6-3, 6-2 win over Garbine Muguruza on Monday to reach the Australian Open quarterfinals.

The top-ranked Williams was pushed all the way by No. 24-seeded Muguruza, who matched her in the heavy-hitting rallies, and who conceded only four games to her in the second round of the French Open last year.

Williams appeared to be laboring at times, and had a serious cough. She struggled with her serve in the first set, but found her range in the second.

She will next play Dominika Cibulkova, who reproduced the kind of tennis that helped her reach the final last year as she beat two-time champion Victoria Azarenka 6-2, 3-6, 6-3 in the fourth round.