With Coronavirus making this the first Grand Slam to be played behind closed doors since the start of the pandemic, both players walked out to an empty Louis Armstrong Stadium in New York.
Having reached the semi-finals of last year's French Open, Anisimova has gone deeper in a Grand Slam than her older opponent.
However, this mattered little with Sakkari in reasonably good form of late and closing in on the world's top 10, her experience ultimately showed in swatting the teenager aside.
The match began fairly evenly with both players holding their serve whilst at two games all in the opening set.
This all changed in the fifth game of the set, as Anisimova lost concentration to gift Sakkari several cheap points. The 19-year-old was caught flat footed whilst serving and volleying as the Greek number one rifled a forehand winner passed her onrushing opponent.
The American saved one break point but further pressure from the Greek threw up a second break point, and a sloppy double fault from Anisimova gave Sakkari the crucial break and she never looked back.
The 25-year-old held serve to move 4-2 up. A solitary hold from Anisimova kept things interesting to make it 4-3. Sakkari then continued to hold without facing a break point as she stormed 5-3 up.
A clutch of forehand errors from Anisimova gave Sakkari three set-points. The 19-year-old American dumped a backhand into the net to surrender the opening set as the Greek secured her second break of the match.
Anisimova, seen as one of the bright stars in American tennis, responded with an immediate break at the beginning of the second set, secured with a rasping aerial forehand winner.
But this was as good as it got for the youngster as Sakkari immediately broke back and secured the double break as Anisimova's head dropped.
Sakkari continued to motor towards the finish line as she despatched the 22nd seed, without breaking a sweat, to wrap up the win.
Maria Sakkari looking 💪 pic.twitter.com/yDioDvtepJ— US Open Tennis (@usopen) September 5, 2020
After the match, the Greek admitted her delight especially having seen childhood friend Stefanos Tsitsipas exit from the men's last night, in a shock loss to Croatian Borna Coric. Her victory maintains Greek interest in the tournament.
Next up for Sakkari is another American, with 2017 champion Sloane Stephens up against 23-time Grand Slam champion, Serena Williams, in the all-American clash on Arthur Ashe later today.