Lebanon coach Michael Cheika said, "I'm super proud of the boys. I don't say that lightly."
He said fatigue affected the finish and some part-time players handled the conditions well.
Error-free in the first half, Lebanon had early chances but will end its campaign against France next Sunday.
Tonga made 13 errors and were without Isaiya Katoa, Robert Toia and Tyson Frizell, six days after beating England in Perth.
Sione Katoa and Jojo Fifita each scored twice in the final 10 minutes.
Tonga remain unbeaten in the Rugby League World Cup but have not secured a semi-final berth.
Samoa play Papua New Guinea in Port Moresby on Saturday before facing Tonga next Sunday.
"It's a huge game for both countries given the history between Tonga and Samoa. We're expecting another physical game and we're looking forward to it," Tonga skipper Jason Taumalolo said.