The British number three will now begin the Grand Slam with a match against 31st seed Daniela Hantuchova at 00:00 GMT on Monday.
Watson took two hours and three minutes to close out the two sets as she aims to get her career back on track following a frustrating 2013 which was blighted by glandular fever.
She reached round three in last year’s event, and admitted after beating Falconi that failing to reach the first round proper this time around would have seriously affected her confidence for the rest of 2014.
"It would have been the end of the world if I didn't get through," the 21-year-old told BBC Sport.
"I'm very happy that I am through but this is where it starts. I've just got over that first hurdle and there's a long way to go yet."
Watson used a neat backhand to clinch the opening set having just missed out on the chance to serve it out at 5-4, before fighting back from an early break in set two.
Despite saving further break points, however, she was unable to keep her accuracy strong during two match points and was forced into a tense tie-break.
An early double-fault from Falconi gave Watson the chance she needed to resume control and the Guernsey girl took it with both hands by nailing seven straight points to reach the main draw.
"It was a very tricky match," explained 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."