Williams turned it on down the stretch, winning the final four games of the final set to outlast Azarenka 6-2, 2-6, 7-5 at Arthur Ashe Stadium in Flushing Meadow.
It was the 15th career Grand Slam title for the fourth-seeded Williams and her fourth victory in six finals appearances in New York, but her first title there since 2008.
Last year, Williams was outset in the final by Australia's Samantha Stosur.
The match had been set for Saturday, but was washed out due to heavy rain and strong winds in New York.
Azarenka -- appearing in her first-ever U.S. Open final -- was seeking her second career Grand Slam title as well as her second of 2012 after winning the Australian Open in January.
She reached the final by besting Russia's Maria Sharapova Friday, 3-6, 6-2, 6-4. Azarenka also topped Sharapova in the Melbourne finale.
Williams, meanwhile, gained the championship round with a 6-1, 6-2 rout of Italy's Sara Errani in Friday's semifinal.
She collected her 14th career Grand Slam title at Wimbledon in July and followed that up with an Olympic gold medal last month in London.