Moore joked on social media that the comeback was "never in doubt".
Moore's feat is not the greatest comeback however.
That accolade probably belongs to American teenager Barbie Bramblett who was down 0 - 6, 0 - 5, 0 - 40 against Ann Hulbert in a 1983 US Open qualifier. She saved 18 match points to go on and win that contest.
"Obviously I thought the match was over, and I was so embarrassed," said Bramblett, reflecting on the game nearly 30 years later.
"So I started swinging out on the ball, and my game elevated miraculously. I mean it was a literal miracle. Every ball I hit skidded on the line. I couldn't believe what was happening."
Other great comebacks include the 1987 classic, when American legend Jimmy Connors beat Swede Mikael Pernfors after trailing 1 - 6, 1 - 6, 1 - 4.
At the 1995 French Open, Czech Jana Novatna was leading American Chanda Rubin 5 - 0 and 40 - 0 in the deciding set. Rubin went on to win, saving nine match points.