Moore put her dreadful first set behind her at the start of the second, breaking the Russian and then held her own serve despite facing break points to warm up the crowd.
She then stunned Kuznetsova by breaking her again in the third game to put herself in control of the set.
Then, after all that good work, Moore produced a sloppy service game and handed back a break only for her opponent to deliver another series of ground stroke errors to put her 1-4 down and the set went to the British player 6-2.
Kuznetsova imposed herself early in the third, breaking Moore to lead 3-0 only for the British right hander to start firing off ground stroke winners with confidence to fight her way back into the set.
Wimbledon 2016 - In pictures
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Despite saving one match point, she eventually fell to her more experienced opponent.
Defending champion Serena Williams survived a first scare against Christina McHale before winning 6-7, 6-2, 6-4.
