Li was broken again in the ninth game to give Azarenka a 5-4 lead and she served out to love in the next game to send it into a decider when a Li forehand sailed wide.
Both had problems settling again after the interruptions to the third set but Azarenka achieved the crucial break and was able to hold things together long enough to earn her second grand-slam title when a Li forehand sailed long over the baseline.
"I have to congratulate Victoria, a fantastic result in two years," Li said before she thanked her coaching team.
"Thanks to the team, two weeks ago I really had to say I hate my team because they pushed me a lot.
"But I think it's not bad, so I should shut up and continue.
"So, I know I'm not young, I still have to say I'm looking forward to next year."
In Image: China's Li Na is escorted back to her chair by medical staff after falling for a second time during her match against Victoria Azarenka of Belarus