U's substitute Marcus Bean had earlier cancelled out a David Mooney goal that put the promotion chasers in front before Odubajo had the final say, but Wolves' 3-0 win over Port Vale means they now lead the table on goal difference.
The home side looked far from convincing despite taking the lead after 21 minutes. Dean Cox crossed into the box and the ball fell to Mooney, who unleashed an unstoppable volley into the net from 15 yards for his 16th league goal of the season.
Both teams were evenly matched in the first half but after the break the visitors dominated the play.
Eldin Jakupovic was called into action within a minute of the restart and the on-loan Hull goalkeeper pulled off two stunning saves at point-blank range to protect the O's lead.
Jakupovic was also quickly off his goal-line to rob Macauley Bonne before the visitors gained a deserved equaliser after 79 minutes, left-back Ryan Dickson crossing for the unmarked Bean to head home from close range.
However, just four minutes later Orient restored their advantage when substitute Shaun Batt played Odubajo in and the 20-year-old steered the ball home with some aplomb.