Fullback Morea Morea also starred for the Kumuls against the gallant Karmichael Hunt-coached Aitu on Saturday.
Halfback and captain Lam had two try assists and controlled play, Morea dazzled at the back and Bai steamrolled.
The Gold Coast 18-year-old, the son of PNG legend Marcus Bai, appears set for a lengthy NRL and international career.
PNG will now play Fiji next week to decide the Pacific Bowl winner.
Cook Islands have their sights on the World Cup qualifier against South Africa on November 9.
This Pacific Bowl competition has been an opportunity to fine-tune combinations and there has been a lot to like.
The Aitu were more than competitive and took an early lead when hooker Rua Ngatikaura darted over from dummy-half after throwing a dummy.
Kumuls try-scoring machine Robert Derby raced 60m to score his seventh try in just his seventh Test.
Cook Islands veteran Reubenn Rennie has been a star for French side Toulouse and he continued his strong Pacific Bowl with a powerhouse try.
Lam showcased his class to put second-rower Rhyse Martin over to level the scores at 12-all.
Derby got his second try after a slick pass by Morea. The try came not long after a barnstorming run by Bai.
Bai was cheered each time he touched the ball by the partisan crowd.
Morea stripped the Cook Islands defence for numbers with another classy ball for fan favourite Alex Johnston to cross in the corner.
The Aitu refused to go away and when Esan Marsters, playing at halfback, put Esom Ioka over there were only six points in it with 20 minutes to go.
Morea appeared to have sealed the match with a try of his own but Marsters put a steamrolling Delahia Wigmore over to give the home crowd a nervous final six minutes.
Kumuls five-eighth Gairo Voro sealed the win with the final play of the match with an intercept try.
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