In the 11th minute Odubajo was again denied by Flinders before the Hartlepool goalkeeper made another save, this time from Jimmy Smith.
Ryan Brunt shot wide for the home side after 37 minutes as they were still unable to break through.
Steve Howard could have broken the deadlock for the visitors with their first proper chance on 40 minutes, but his shot was saved by Ryan Allsop.
Just two minutes into the second half Orient were finally ahead. Odubajo was naturally involved, and it was his cross that Ryan Brunt headed home.
Flinders was again called into action on 50 minutes, this time keeping out a Dean Cox effort.
Orient managed to hold on to their clean sheet and took an important 1-0 win.