MELBOURNE — Once again Li Na had the Rod Laver Arena crowd on its feet, roaring — this time with laughter.
Her encore to a 7-6 (7-3), 6-0 win over Dominika Cibulkova in the Australian Open title match Saturday night made her even more popular at Melbourne Park, where she’d lost two finals in the previous three years. So she paid her supporters back with one of the best of her improv stand-up routines.
First she thanked her agent ‘‘for making me rich,’’ then her coach Carlos Rodriguez, and then her husband Shan Jiang — her former coach and constant traveling companion.
‘‘Thanks for him giving up everything just traveling with me to be my hitting partner, fix the drinks, fix the racket — so thanks a lot, you are a nice guy,’’ she told Shan in a rare public compliment, pausing for the laughter. ‘‘Also you are so lucky [to] find me.’’
Li, who will turn 32 next month, is the oldest women’s champion in Australia in the Open era. She didn’t see age as a barrier, replying to a question on the topic with a smile and an opinion: ‘‘I’m not old!’’
‘‘Yeah, start of tournament everybody talking about the age. I would like to say age is nothing,’’ she said. ‘‘Still can win the Grand Slam. So pretty happy about my age. I got more experience on the court.’’
Li lost Australian Open finals to Kim Clijsters in 2011 and to Victoria Azarenka last year, when she twisted her ankle twice in the second and third sets and needed a medical timeout after hitting her head on the court. In between, she won the 2011 French Open in one of the many firsts she’s established for Chinese tennis.
Yet it was a defeat that almost had the biggest impact on her career, with heavy criticism in the domestic media following a second-round loss at last year’s French Open sending her to the verge of retiring.
Rodriguez, who previously worked with Justine Henin, had to talk Li into playing Wimbledon, encouraging her to just see how she progressed at the All England Club before making such a big career decision. She responded by reaching the quarterfinals at Wimbledon, the semifinals at the US Open, and now breaking her drought in Australia. She paid tribute to Rodriguez’s calm, composed approach and support.
‘‘Before the match he was telling me to relax, just think it’s a match, don’t think it’s a final,’’ she recounted, admitting that she’d even taken time out for a short afternoon sleep. ‘‘He always say, ‘Believe in yourself.’ He always believed in me, I never believed in myself. That was my problem.’’
In both her previous finals at Melbourne Park, Li won the first set but went down in three.
She had no such trouble against No. 20-seeded Cibulkova, who was playing in her first major final.
Li opened the final by breaking Cibulkova, holding, and then getting a break-point chance in the third game. But Cibulkova held, and then broke back in the sixth game thanks to a pair of double faults from Li. Another service break followed, and Li had a set point before losing three straight points to ensure it went to the tiebreaker. As the second set began, a fan in Rod Laver yelled, ‘‘C’mon Li Na, bagel her!’’
A half-hour later she was holding up both thumbs to the crowd, and holding back tears as she hugged her Slovakian rival. The diminutive Cibulkova, one of the shortest players ever to reach a Grand Slam final at 5 feet 3 inches, had four wins over top-20 players on her way to the final, including a fourth-round upset of third-seeded Maria Sharapova and a straight-sets semifinal trouncing of No. 5 Agnieszka Radwanska.
‘‘These were just a fantastic two weeks of my life,’’ she said. ‘‘Hello to everybody in Slovakia. This means a lot for our country and I’m happy I can be the one here for Slovakia.’’
No. 4-seeded Li, who reportedly has four times more followers on her Chinese social networking site than there are people in Slovakia, had a good run through the tournament as other star players such as Serena Williams, Sharapova, and Azarenka tumbled out by the quarterfinals.
She didn’t have to face a player ranked in the top 20 en route to the final, opening with wins over the two youngest players in the tournament, then saving a match point in her third-round win over Lucie Safarova, who was a fraction away from causing a major upset.
‘‘I think I should send e-mail to Safarova,’’ Li said. ‘‘Sorry . . . and send smile to her as well.’’
Now she’s already promising to come back and defend her Australian title. ‘‘Finally I got her,’’ Li said as she put a hand on the Daphne Akhurst Memorial Cup for the first time. ‘‘Last two times were very close.’’
. . .
Lukasz Kubot and Robert Lindstedt won the men’s double title in their first Grand Slam as a team with a 6-3, 6-3 win over American Eric Butorac and South Africa’s Raven Klaasen.
Butorac, who lives in Boston, and Klaasen had an upset win over top-ranked Bob and Mike Bryan in the third round. In the first round, they beat local favorite Pat Rafter, who came out of retirement at the age of 41 to play doubles with Lleyton Hewitt.
‘‘I never dreamed that I would actually play in [the Australian Open] and to be here playing in a Grand Slam final was an absolute dream come true,’’ Butorac said.