Gutsy Venus Williams saved five match points before her 21st US Open campaign was ended by Elina Svitolina.

Serving to stay in the match, the 39-year-old American showed her never-say-die spirit remains undimmed in a marathon penultimate game.

She forced Svitolina to serve for the match, the Ukrainian fifth seed eventually crossing the line for a 6-4 6-4 victory.

"It was a really incredible match," said Svitolina.

"It was really special. It's unbelievable what Venus does, on and off the court she is a big inspiration.

"I had to stay very focused and try to put an extra ball over the net. She knows how to handle moments like this, it was incredibly tough and only a few points decided the match."

Third seed Karolina Pliskova is also through to the third round, the 27-year-old from the Czech Republic beating Georgia's Mariam Bolkvadze 6-1 6-4.