Serving to avoid a "double-bagel" humiliation against French third seed Jessika Ponchet, Moore fell 30-40 behind on her own serve in the first round of the ITF World Tennis Tour event in Sunderland on Tuesday.
But the luck of the 479th-ranked player began to change when her overhead smash clipped the net and bounced on the line.
Moore, 26, pulled herself back into the match, winning the second-set tie-break and went on to complete a 0-6, 7-6 (9/7), 6-3 victory over the player ranked nearly 300 places above her.
After the result Moore tweeted that the result was "never in doubt" in response to a video clip of her lucky net cord winner.
"Thank you everyone for the kind messages the support has been overwhelming," she said in another tweet.
"Hope I can just inspire all the young boys and girls (and adults) to never give up and keep on fighting #neverindoubt."
Hong Kong-born Moore, who reached the second round at Wimbledon in 2016, was due to play Germany's Yana Morderger in the second round of the $25 000 tournament on Thursday.