The home side went ahead after 14 minutes when Boro goalkeeper Chris Day blocked a shot from Dagnall only to see the ball rebound to Odubajo, who stabbed home from close range.
Dagnall doubled the advantage after 23 minutes, strike partner David Mooney robbing Luke Jones before squaring the ball into the path of his fellow striker for the simplest of chances.
Dagnall and Odubajo both had chances to increase their tallies before the break but the visitors improved after the interval to cause the home side a few anxious moments.
Substitute Darius Charles twice came close to reducing the deficit while Michael Doughty was denied by a full-length save from O's on-loan 'keeper Eldin Jakupovic.
But Orient held out to move above Wolves on goal difference and occupy second place in the race for promotion.