UNFORCED ERRORS ... Anne Keothavong
The sixth seed and Olympic champion Dementieva beat 87th-ranked Keothavong 6-3 6-4.
But the match was far from straightforward for the Russian, who could become women’s No 1 if she wins in New York.
Keothavong, 24, served to take a 5-3 lead in the second set and should have taken the match into a decider before a run of silly mistakes.
Dementieva, 26, said: “Anne can reach the top 40, maybe even better. She gave me problems.
“She was not afraid, she played aggressively, and is the best British player I’ve ever played.”
Keothavong, who only broke into the top 100 this year, said: “I had chances but hit too many errors. But it’s been a good week.”
The Londoner had trouble getting a table at her lucky French restaurant before her match.
She said: “There were some people at the table where we’ve been eating but they let us sit there.
“Unfortunately, it didn’t do me a lot of good.”