Odumbe, whose international future hangs in the balance, came to the crease when the homeside were four wickets down and partnered Ravindu Shah to bring up the score to 360 for four at the close on Thursday.
But it was Shah who stole the limelight. The Kenyan innings were built around the right-hand batsman, who finished with a brilliant 170 not out after leading from the start.
With opening partner Kennedy Obuya, Shah put on 105 runs for the first wicket before Obuya was caught behind by the Pakistan wicketkeeper Kamran Akmal.
Akmal also took account of the Kenyan captain Steve Tikolo. Tikolo, on 80 was racing to his second century of the series when he was caught behind off the bowling of Junaid Zia who took two wickets in the match.
Kenya will resume their batting on Friday.