Azarenka took a seesaw 4-6, 6-4, 6-3 decision, fittingly finishing the championship with her ninth break of the match.
The win gives Azarenka two Grand Slam titles. It was a victory over Maria Sharapova in the 2012 Australian Open final that moved Azarenka to the top of the rankings for the first time. The win Saturday allows her to keep the No. 1 ranking, which would have gone to Serena Williams had Azarenka lost.
Li was the fan favorite throughout Saturday's final, only strengthening the support as she twice was injured in the match. She rolled her left ankle midway through the second set and fell and hit her head hard on the court in the third.
The 2-hour, 40-minute match was decided by service breaks, however. There were a total of 16 in the 29 games.
Thick fog, play suspended at Torrey Pines
LA JOLLA, Calif., Jan. 26 (UPI) -- Third-round play at the Farmers Insurance Open was suspended Saturday due to thick fog at Torrey Pines after just one threesome finished a single hole.
Each shot par to remain at 3-under par for the tournament.
Play was to be resumed Sunday morning with a Monday finish likely.
Tiger Woods -- looking for his seventh career victory at Torrey Pines -- grabbed a two-stroke lead Friday with a 7-under 65, and remained the leader at 11-under-par 133.
Cubs tepid on rooftop billboard proposal
CHICAGO, Jan. 26 (UPI) -- The Chicago Cubs reacted coolly to the idea of putting billboards on buildings across from Wrigley Field used as rooftop grandstands for baseball fans.
The owners of the rooftops seating made the proposal this week as an alternative to the team's plan to erect outfield billboards on the stadium itself, which would effectively block the views from the rooftops.
The rooftop owners have threatened to sue. The Cubs, however, appeared unmoved the compromise proposed this week.
"If the rooftop owners have a new plan, they would be well advised to discuss it with the team instead of holding press conferences, because a deadline is fast approaching for the team and the city of Chicago to move forward," Dennis Culloton, a spokesman for the Cubs ownership, told the Chicago Tribune.
Lindsey Vonn narrowly wins giant slalom
MARIBOR, Slovenia, Jan. 26 (UPI) -- Lindsey Vonn of the United States edged Slovenia's Tina Maze by .08 seconds to win the women's World Cup giant slalom Saturday.
Vonn used a heroic second run to move up from third place and turn in a combined two-run time of 2 minutes, 22.20 seconds on the Gold Fox course in Maze's home-country Maribor.
Anna Fenniger of Austria was third followed by Germany's Maria Hoefl-Riesch.
Maze, the overall women's World Cup points leader, admitted to a slight glitch near the top of her second run but was pleased to be on the podium. "It is an incredible feeling to race in front of so many people cheering for you! I could hear them from top to bottom," she said. "Of course it is not easy to race when everybody expects you to win."
Maze extended her lead in the point race. She increased her total to 1,554 points. Hoefl-Riesch remained a distant second with 748 points.
Notable deaths of 2014 [PHOTOS]