The only goal in the return match came from Elliot Lee in the 21st minute.
West Ham, who finished 12th in the Premier League last season, had to play with 10 men for more than 75 minutes after forward Diafra Sakho was dismissed following a clash with a Lusitans defender.
Bilic's team must progress through three more rounds to reach the Europa League group stages. The second qualifying round begins next week.
(Story refiled to correct spelling of Lusitans throughout)
(Reporting by Tom Hayward, editing by Tony Jimenez)
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