American Williams, 38, stopped Rus serving out the match at 6-5 before winning 7-6 (8-6) 3-6 7-6 (7-0) in nearly three hours.
"I had a crowd in my head or something".
The world number 10 was playing her first match since the WTA resumed after it was suspended because of the coronavirus pandemic.
Playing in her second tournament since the tennis season restarted, Williams won 7-6 (8-6) 3-6 7-6 (7-0) against the world No 72 in a gruelling contest that lasted almost three hours.
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Rus was able to mount a defence against Williams with a combination of left-handed baseline stokes.
Favoured to win the U.S. Open, Serena Williams found herself having to fight to stay alive during the Round of 32 on Monday at the Western & Southern Open. That saw Williams struggling and giving up four back-to-back games during the second set and again in the third, which ultimately forced the tiebreaker.
After working her way into the main draw through qualifying, Rus came in match sharp while Williams looked sluggish on a hot and humid NY afternoon.
Earlier, No. 2 seed Dominic Thiem, a three-time major finalist, wasn't much more competitive in a 6-2, 6-1 loss to Filip Krajinovic, and No. 5 Alexander Zverev hit 11 double-faults - five over his last two service games - while being beaten by Andy Murray 6-3, 3-6, 7-5.
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The drama started on Thursday, Aug. 20, when McGowan posted a tweet calling out the Democratic Party and its track record. The couples stepped onto an outside stage and embraced as they watched the fireworks light up the sky.
"I'm actually super fit and I'm super ready", she added.
Williams' matches are a magnet for fans but with no spectators allowed onto the Billie Jean King National Tennis Center grounds due to COVID-19 safety protocols, the atmosphere inside a steamy Grandstand was one of relief rather than excitement as the 38-year-old American trudged off following the hard-fought victory. If there were the usual crowd of thousands when Williams plays, Sakkari calculated, the fans' support would break down along these lines: "99% with her, 1% with me".
She moved into the third round thanks in part to 14 aces, one at 121 miles per hour.
Awaiting Williams, a two-time victor of the event, in the last 16 is Maria Sakkari after the Greek 13th seed beat Yulia Putintseva 6-4 7-6 (11-9).
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Top seed Karolina Pliskova and No. 2 Sofia Kenin both bowed out in second-round openers - and it looked like 23-time Grand Slam champion Williams could follow them before she roared back to beat Rus 7-6 (8/6), 3-6, 7-6 (7/0).