2015 photo by Paul Bauman
Agnieszka Radwanska trailed 5-2 in the final set.
And Tomas Berdych was extended to a fifth set.
All three high seeds, however, advanced to the quarterfinals of the Australian Open in Melbourne.
Djokovic, the top seed and defending champion seeking his sixth Australian Open title, subdued 14th-seeded Gilles Simon of France 6-3, 6-7 (1), 6-4, 4-6, 6-3 today (PST) in 4 hours, 32 minutes.
Radwanska, seeded fourth, rallied to beat unseeded Anna-Lena Friedsam of Germany 6-7 (6), 6-1, 7-5. The 82nd-ranked Friedsam, who will turn 22 on Feb. 1, struggled with leg cramps in the last three games.
Berdych, the No. 6 seed, outlasted No. 24 Roberto Bautista Agut of Spain 4-6, 6-4, 6-3, 1-6, 6-3 to reach the quarterfinals for the sixth straight year.
Djokovic advanced to his 27th consecutive Grand Slam quarterfinal, tying Jimmy Connors for second place in the Open era behind Roger Federer (36).
Djokovic will face No. 7 seed Kei Nishikori of Japan in the quarters. Nishikori dismantled No. 9 Jo-Wilfried Tsonga, the runner-up to Djokovic in the 2008 Australian Open, 6-4, 6-2, 6-4.
Berdych will meet No. 3 seed Federer, a four-time Australian Open champion who outclassed No. 15 David Goffin of Belgium 6-2, 6-1, 6-4.
2014 photo by Paul Bauman
Both Gavrilova, a 21-year-old Moscow native, and Suarez Navarro, a 27-year-old Spaniard, have won doubles titles in Northern California.
No. 1 seed Serena Williams, the defending and six-time champion, and No. 5 Maria Sharapova, the 2008 titlist, won in straight sets to set up a rematch of last year's final.
Williams, a three-time Bank of the West champion, is 18-2 against Sharapova, the Stanford runner-up in 2010, with a 17-match winning streak.
Meanwhile, Lleyton Hewitt's career ended with a loss in the third round of doubles. No. 9 seeds and 2014 Wimbledon champions Vasek Pospisil of Canada and Jack Sock of Kansas City, Mo., defeated Australia's Sam Groth and Hewitt 6-4, 6-2.
Hewitt won the now-defunct San Jose stop on the ATP World Tour in 2002 and reached the final there in 2006.
In the first round of mixed doubles, Alla Kudryavtseva of Russia and Robert Lindstedt of Sweden edged seventh-seeded Raquel Atawo (formerly Kops-Jones) of San Jose and Raven Klaasen of South Africa 6-7 (4), 6-2 [10-4].