The world No. 55 beat Sara Errani 6-4 3-6 6-0 in two hours and 16 minutes and will face the Czech Republic's Barbora Strycova in round two.
Any Brit inside the top 56 players in the singles rankings would be guaranteed qualification, subject to BOA ratification, which is very much on Watson's mind.
"It was totally on my mind as we started that third set today," she said.
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"It's just a big goal of mine and with it in the back of my mind it just motivates me and gives me that little bit extra.
"The Olympics is every four years, it's for your country. I can't even describe the atmosphere, it's unbelievable, and I just love being around the other athletes."
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