The 40-year-old Williams was again buoyed by a loud crowd at a full Arthur Ashe Stadium, just as she was in the first round two days earlier.
She hit serves at up to 119 mph, stayed with Kontaveit during lengthy exchanges of big swings from the baselines and conjured up some of her trademark brilliance when it was needed most in a 7-6 (7-4) 2-6 6-2 victory.
When asked after the win if she was surprising herself with her performances, Serena gave the courtside a sly look as if to say “of course not”.
After pulling out a tight first set, then faltering a bit in the second, Williams headed to the locker room for a bit of a break before the third.
Something had to give, someone had to blink.
When they resumed, it was Williams who lifted her level and emerged as the better player.
Just as she’s done, so many times on so many stages, with so much at stake.
The six-time champion at Flushing Meadows will play Friday for a spot in the fourth round.
Her opponent will be Ajla Tomljanovic, the 29-year-old Australian who beat Russian Evgeniya Rodina 1-6 6-2 7-5 in an intense baseline slugfest.
Third-seeded Greek Maria Sakkari had earlier become another big casualty in the women’s draw, falling to a 3-6 7-5 7-5 defeat to unseeded Chinese Wang Xiyu in an absorbing second-round contest.
Sakkari, a semi-finalist in New York last year, took charge in the early stages of Wednesday’s match and marched into a one-set lead before being let down by a series of unforced errors as Wang claimed her first career victory over a top-10 player.
Despite Sakkari’s superior experience, Wang’s heavy hitting from the baseline came to the fore in the second set as she took a 5-3 lead before clinching it following a double fault from Sakkari.
Both players matched each other in the decider but it was Wang who raised her game in the key moments, breaking Sakkari at 6-5 to take the win and reach the third round of a grand slam for the first time.
Sakkari’s defeat capped a difficult couple of days for Greek tennis following the shock first-round exit of men’s fourth seed Stefanos Tsitsipas at the hands of Colombian qualifier Daniel Elahi Galan.