You are not permitted to download, save or email this image. Visit image gallery to purchase the image.
The 23-time Grand Slam winner came up short in the second-set tiebreak, with her power serve abandoning her when she needed it most.
Sakkari carried the momentum into the third set as she started the decider with a break.
But the 38-year-old American once again showed the battling instincts that has made her one of the all-time greats. She broke back to level for 2-2 as Sakkari's forehand started to misfire.
The six-time Flushing Meadows champion marked her 100th win on Arthur Ashe Stadium with a roar that could be heard all around the grounds.
"I just kept fighting," said Williams, who lost to Sakkari two weeks ago in the Western & Southern Open.
"She was doing so well she was being so aggressive.
"I knew I needed to do the same thing."