The 26-year-old capped a remarkable tournament with a 6-2 7-5 victory over Japan's Taro Daniel in Saturday's final.
So unexpected was his run that his coach Guillermo Gomez had been waiting for him in Melbourne and was forced to fast-track a visa application to arrive in New Zealand in time to watch Tabilo lift the trophy.
"It honestly feels surreal ... so happy, very emotional," Tabilo said of his triumph.
"(I) honestly never thought we'd be here in the final. In the quarters we just applied for (the visa). Crazy, crazy story."
Tabilo, expected to soar from No.82 in the world to inside the top 50 after this week's performance, raced through the opening set after being locked at 2-2.
He endured a sterner test in the second set, but came through to become the first Chilean man to claim a hardcourt tour-level title since Fernando Gonzalez in Beijing in 2007.
Up next for Tabilo is a first-round match against American Aleksandar Kovacevic at the Australian Open on Monday, while losing finalist Daniel will take on world No.34 Christopher Eubanks.
The year's first grand slam begins in Melbourne on Sunday.
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