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.”
Thiem crushes Augur-Aliassime to reach U.S. Open quarters
Second seed Dominic Thiem edged a first-set tiebreak before turning up the heat to romp into the U.S. Open quarter-finals with a resounding 7-6(4) 6-1 6-1 victory over Canadian youngster Felix Augur-Aliassime at Arthur Ashe Stadium on Monday.
Top seed Novak Djokovic’s disqualification on Sunday for striking a line judge with a ball has left Thiem as one of the favourites and the Austrian gave a composed performance to reach the last eight in New York for the second time in his career.
He was helped in his quest for a maiden Grand Slam title by a below-par performance from Augur-Aliassime, who beat Andy Murray in round two but was well off the pace against Thiem, making 51 unforced errors compared to the second seed’s 24.
Thiem won 74% of his first serve points and was near flawless at the net, while also sending down 22 winners as he wrapped up the contest in a shade over two hours.