Defeat in qualifying this time would have come as a major blow both to her ranking and her confidence, but she battled through in two hours and three minutes.
"I'm very happy that I am through but this is where it starts," said Watson.
"I've just got over that first hurdle and there's a long way to go yet."
After admitting to feeling nervous in her opening two qualifying matches, the tension was ratcheted up against Falconi.
The 23-year-old American is a friend and practice partner of Watson, who knew she would have to face a mixture of slice, volleys and lobs.
Watson feeling 'stronger' than ever
Watson failed to serve out the first set at 5-3 but looked to be on course when she clinched it with a clever backhand slice in the following game.
The Briton recovered an early break in the second and fired down three aces to save break points at 3-3, but when two match points arrived she failed to keep the ball in play and the nerves took hold.
There appeared every chance that Falconi would take the match into a deciding set, but the American faltered in the tie-break with an early double fault, and Watson reeled off seven straight points to clinch a vital win.
"It was a very tricky match," added Watson. "She's not your usual WTA player. She slices a lot, she's got good hands, good touch, she's not the overpowering type.
"I was prepared for it but I was torn between, 'Do I go for it, or do I make her play?'.
"I was finding it difficult to find the balance but I held my nerve at the end - at the very end!
"I got a bit nervous closing it out but it's last round of qualifying; there's a lot on that match."
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