Palace new boys Fraizer Campbell and Brede Hangeland were not involved as they instead featured for an Eagles' XI at Forest Green Rovers, but the Premier League side still took a strong squad across London, including 11 players that played in the final game of last season against Fulham.
Brentford had marginally the better chances of an entertaining first half, however, Andre Gray twice going close, and they eventually made their superiority pay two minutes into the second half when Jonathan Douglas curled home from 15 yards after beating two Palace defenders.
Gray doubled the home side's lead with a fine finish from the edge of the area in the 54th minute but the second goal seemed to shock Palace into life as they scored twice within the space of three minutes to quickly draw level.
First Glenn Murray scored from close range after Brentford had failed to deal with Yannick Bolasie's ball into the box, and then Marouane Chamakh converted an even easier chance after Joe Ledley’s shot was spilled by David Button in the Bees' goal.
Tony Pulis' side may have expected to go on and win the game from there but Odubajo sent the home fans home happy when he lifted the ball over Joel Ward and calmly slotted past Julian Speroni.
Brentford begin life in the Sky Bet Championship against Charlton next weekend, while Palace continue their preparations for the new season with a friendly against Bundesliga outfit Augsburg.