Serena Williams reaches Western and Southern Open third round
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 almost three hours.
Two-time champion Williams will play Greece's 13th seed Maria Sakkari in the third round.
Fourth seed Naomi Osaka of Japan beat Karolina Muchova 6-7 (5-7) 6-4 6-2.
The world number 10 was playing her first match since the WTA resumed after it was suspended because of the coronavirus pandemic.
Osaka will face 16th seed Ukrainian Dayana Yastremska in round three.
It was a far from convincing performance from
Williams, who appeared to struggle in the New York heat in the second set, and failed to serve out victory at 5-3 in the deciding set.
"It was a real physical match," said 23-time Grand Slam champion Williams.
"I played pretty well, I was being aggressive and hit some good shots, but she just kept fighting."
Williams, ranked ninth in the world, will be looking for a record-equalling 24th Grand Slam title when the US Open starts on August 31 at Flushing Meadows.
It will be the first major since the professional tours resumed earlier this month, having been suspended in March because of the coronavirus pandemic.
The Western and Southern Open is usually held in Cincinnati but has been moved to Flushing Meadows to create a two-tournament safety bubble.
Williams, seeded third, is the highest-ranked player left in the draw after Czech top seed Karolina Pliskova and American Sofia Kenin lost their opening matches.