Williams, a seven-time singles and 14-time women’s doubles Grand Slam champion, is playing her 25th US Open.
She won the first of her two women’s doubles titles in New York with younger sister Serena in 1999, three years before Fernandez was born.
Addressing Williams in her on-court interview, former US Open singles runner-up Fernandez said: “Seeing you play on court with the same big smile you had back then is so inspirational and motivates me to keep going. I love that you love tennis.”
It is the first time that Williams has reached the quarter-finals of a major since winning the Wimbledon title, also alongside Serena, in 2016.
Asked if she had a message for her younger sibling, Williams joked: “She’s so happy for Leylah and I, she’s given us advice and we just need her in the box, so my message is ‘Serena, you need to show up!'”
Their quarter-final opponents could be top seeds Katerina Siniakova and Taylor Townsend, whose third-round match had not begun when Williams and Fernandez left the court having signed autographs for many of their waiting supporters.
For Alexandrova, it was the second defeat of the day on Louis Armstrong Stadium, having earlier been knocked out of the singles by Iga Swiatek on the same court.