Shane Dooley finished the game with 1-14.
Tullamore Hurling Manager Shane Hand says his side "deserved" their win against Shinrone on Sunday.
They kicked off their Offaly Senior Hurling Championship campaign with a 2-24 to 3-19 win over last season's beaten finalists in O'Brien Park.
Shane Dooley was top scorer for his side with 1-14, with Mike Fox and Martin Keogh scoring 0-3 each.
Hand says he's pleased with his sides work rate:
Elsewhere, Brian Duignan scored 0-10 as Ballinamere got off to a winning start over Lusmagh as they won 0-24 to 0-12.
Goals from Shane Rigney, Evan Houlihan and Evan Woods secured St Rynaghs their first win of the season over Birr on a scoreline of 3-18 to 1-20.
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