The Tongans scored four first-half tries but were held to a single Ata Hingano penalty after the break and had it not been for two disallowed tries, it might have been Lebanon heading to Auckland to play England or Papua New Guinea next weekend.
Lebanon, inspired by five eighth Mitchell Moses and halfback Robbie Farah, drew within two points of their tiring opponents when Abbas Miski crossed for his second try with 11 minutes to go but could not find another score to register the upset.
"I'm pretty heartbroken at the moment," said man of the match Moses.
"It's just heart-breaking to see how hard the boys worked and to be caught up with some calls that weren't right. We'll hold our heads high but we're broken now."
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Although there can have been little argument when Moses was ruled to have come up short of the line in the 57th minute, the video referee's decision to disallow an Adam Doueihi score six minutes after the break for obstruction was more debateable.
Tonga had started the match as if they were going to reprise the second half of their stunning upset of New Zealand in their final pool match last week.
David Fusitu'a, who scored a hat-trick against the Kiwis last week, added two more to his tournament tally, with stand off Tuimoala Lolohea and fullback Will Hopoate also crossing.
Doueihi and James Elias replied for Lebanon, though, and when Miski finished off a brilliant team move just before the break the underdogs were in touch at 22-16.
"It was really scrappy, we didn't play to our potential but credit to Lebanon, they played a really tough game and really gave it to us," said Tonga captain Sika Manu.
England and Papua New Guinea meet in Melbourne on Sunday.
(Reporting by Nick Mulvenney in Sydney, editing by Peter Rutherford)
