Jiri Lehecka claims first ATP title in Adelaide, Alejandro Tabilo wins Auckland
The Czech reached the quarter-finals of the Australian Open last year and will be battle-hardened for his third trip to Melbourne Park after the tight two-hour contest against fellow 22-year-old Draper.
A single service break was enough to give left-hander Draper the opening set but Lehecka levelled up the contest when he managed the second of the match to snatch the second stanza.
That appeared to knock a bit of the stuffing out of Draper, who was also seeking his maiden tour title, and Lehecka raced to a 3-0 lead in the decider.
Draper, whose career has been blighted by injuries, never gave up the fight and had three break points at 3-1 but Lehecka saved them all and sealed the title with an unreturnable serve after just over two hours on court.
"It's hard for me to say anything because I'm so emotional after winning my first title in Adelaide, I'm so excited," Lehecka said after the trophy presentation.
Lehecka, the 32nd seed, takes on Spaniard Bernabe Zapata Miralles in the first round in Melbourne, while Draper, who lost to Rafael Nadal last year in his only previous match at the Australian Open, faces American Marcos Giron.
Elsewhere, Alejandro Tabilo will head into the Australian Open on a high after winning his first ATP Tour title with a 6-2, 7-5 victory over Japan's Taro Daniel in the Auckland Classic final on Saturday.
The 26-year-old Chilean, who is ranked 82 in the world but is expected to break into the top 50 on the back of his triumph, raced through the opening set after being locked at 2-2.
He endured a sterner test in the second but came through in the end 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. The year's first Grand Slam begins on Sunday.