"I know I am the underdog when I play Lee and usually I would have put pressure on myself. This time I wanted to play my game, joke on court with myself," the 31-year-old said.
Leverdez failed to convert two match points in the second game but kept his composure against a nervy Lee in the decider to grind out the result.
Defeat ended the 34-year-old Lee's hunt for an elusive first title in a competition in which he has been runner-up three times.
"Brice played so well today... he had the lead for a lot of the second game and he was very lucky," Lee said after the match.
Defending champion Chen Long started his campaign with a convincing win over Georges Julien Paul from Mauritius. The Chinese fifth seed downed his opponent 21-7 21-9 in 29 minutes.
Taiwan's Chou Tien Chen survived a scare from England's Toby Penty before winning in three games while Denmark's Hans-Kristian Vittinghus lost to Chinese 10th seed Tian Houwei.
In the women's draw, Japanese top seed Akane Yamaguchi beat Denmark's Line Hojmark Kjaersfeldt 21-6 21-13 in 30 minutes while fourth-seeded Indian Pusarla Sindhu beat South Korea's Kim Hyo Min 21-16 21-14.
China's Sun Yu, seeded fifth, powered past unseeded Indonesian Lyanny Alessandra Mainaky 21-13 21-9 in 47 minutes. She was joined in the second round by compatriot Chen Yufei.
Thailand's Ratchanok Intanon overcame Malaysia's Rui Chen Yap 21-12 21-7 while China's Chen Xiaoxin defeated Canada's Michelle Li 21-13 27-25.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Neil Robinson)
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