Williams hardly looked like the reigning Wimbledon champion against the 20-year-old Suarez Navarro, whose previous best showing in a Grand Slam was reaching the French Open quarterfinals last year. [break]
Looking increasingly sluggish, Williams was broken while serving for the match and dropped the last five games.
Suarez Navarro, overmatched at first, broke twice in the second set as Williams let a number of reachable shots fly past. She saved a match point while serving at 4-5 in the deciding set and broke Williams in the next game, aided by a double-fault from the American.
Suarez Navarro squandered one match point while serving at 40-15 in the next game before Williams netted a forehand for her 37th enforced error.
Serena Williams, on the other hand, ignored pain and frustration to reach the third round with a straight-sets win over Gisela Dulko.
The second-seeded Williams´ 6-3, 7-5 victory was far from routine, unlike Rafael Nadal´s 6-2, 6-3, 6-2 win over Croatia´s Roko Karanusic.
Williams, hoping to extend a sequence of winning the Australian title every alternate year since 2003, had to fend off six set points in the ninth game of the second set to prevent the match from going to a third set. That game went to a dozen deuces before Williams broke to get back on serve.
She had a brace removed from her left ankle in the changeover and, although grimacing with pain, held and then broke Dulko again — this game going to deuce a half-dozen times — to get her chance to serve it out.
After all that, the nine-time Grand Slam winner finished with ace on her first match point, advancing in 1 hour, 50 minutes.
"It was a very tough second set, she started playing unbelievable, hitting winners left and right," Williams said. "She had a couple of opportunities but I always felt I wasn´t going to lose." Williams graded her performance a "D-minus."
Nadal had an easier time in his second-round match against Karanusic, fending off the bearded Croat´s six break-point chances and converting on six of the seven opportunities he had.
"The result is good. I think I won without problems, no?" the 22-year-old Spaniard said.
He will next play German veteran Tommy Haas, who beat Flavio Cipolla of Italy 6-1, 6-2, 6-1.
Nadal has won four straight French Open titles on clay, had a breakthrough win over Roger Federer on grass at Wimbledon last year and led the tour in 2008 with a 46-10 record on hard courts. But he has never made a final at the Australian or US Opens — the two majors on hard courts.
No 13 Fernando Gonzalez of Chile, the 2007 runner-up, moved on with a 7-5, 6-3, 6-4 victory over Argentina´s Guillermo Canas.
Similarly, Courageous fifth seed Jo-Wilfried Tsonga survived a 195-minute marathon to down Croatian Ivan Ljubicic 6-7 (4/7), 7-6 (10/8), 7-6 (8/7), 6-2 in the second round.
In a high-quality match played on the Hisense Arena, Tsonga and Ljubicic could barely be separated as they went toe-to-toe in an enthralling contest.
"I played really well out there. I was proud of myself because I was very courageous today," said the Frenchman who enraptured local fans as he won his way to the final of the 2008 Open where he lost to Serb Novak Djokovic.
Also advancing were No. 6 Gilles Simon, No. 12 Gael Monfils, No. 14 Fernando Verdasco, No. 17 Nicolas Almagro, No. 22 Radek Stepanek, No. 24 Richard Gasquet and No. 31 Jurgen Melzer also went through.
Dudi Sela was the first Israeli man to make the third round of a major since 1994 when he beat Romania´s Victor Hanescu 6-3, 6-3, 6-2.
Mario Ancic beat fellow Croatian Ivo Karlovic 5-7, 7-5, 4-6, 6-4, 6-3, knocking out the No. 25th seed.
On the women´s side, Olympic champion Elena Dementieva improved her 2009 winning streak to 12 matches with 6-4, 6-1 win over Iveta Benesova.
Dementieva, who won titles at Auckland and Sydney before the season´s first major, struggled with her serve early but recovered to finish the match in 72 minutes.
The 27-year-old Dementieva reached the French Open and U.S. Open finals in 2004, beaten both times by fellow Russians, and has not returned to the championship of a Grand Slam tournament since.
Her highlight last year was a win over fellow Russian Dinara Safina in the gold medal match at the Beijing Olympics. She was ousted in the semifinals at Wimbledon and the US Open in 2008 and has never advanced beyond the fourth round at Melbourne Park.
Amelie Mauresmo, who won here and at Wimbledon in 2006, rallied for a 4-6, 6-3, 6-2 win over Britain´s Elena Baltacha. Mauresmo, a former No 1 now seeded 20th after an injury-plagued 2008, advanced when Baltacha double-faulted on match point.
Fellow Frenchwoman Virginie Razzano ousted No 14 Patty Schnyder of Switzerland 6-3, 6-1.
Other women advancing included No 12 Flavia Pennetta of Italy, No 13 Victoria Azarenka of Belarus, No 18 Dominika Cibulkova of Slovakia, No 21 Anabel Medina Garrigues of Spain and China´s Zheng Jie, seeded 22nd.
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