Darin Classin's side overcame Bangor in a tight affair last Saturday.
It's now seven wins on the spin for Tullamore in Division 2C after the lastest round of fixtures in the AIL.
A trip up to County Down to take on Bangor returned four points on their final away-day of the year.
Eoin Farrell got on the scoresheet for the midlanders either side of tries by Chris Whittle.
The Offaly club trail Instonians now by nine points after the league leaders enjoyed a bonus point win over Midleton.
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