The British No1 recovered from losing the second set to wrap up an impressive 6-4 5-7 6-3 victory.
Watson, who will now face 29th seed Camila Giorgi in round two, admitted that she suffered from nerves at points during the match.
“I was definitely a bit nervous, I think it showed closing out the second set there, but I kept fighting and was able to play the right way to finish the third set,” Watson told BT Sport.
“I just kept fighting. We both didn’t play our best tennis but it was a good match.”
Meanwhile, fellow Brit James Ward missed out on a place in the main draw at Indian Wells after a 6-3 6-1 defeat by Mischa Zverev in the final round of qualifying.
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