St Rynagh's and Kinnitty also picked up big wins in the competition's opening round.
Kilcormac-Killoughey made an emphatic start to the defence of their senior hurling title in Offaly in the competition's first round over the weekend.
Banagher played host to their meeting with Tullamore on Friday evening where it finished 1-36 to 0-13.
Adam Screeney top-scored in the game with 1-9, seven of which were frees, while Shane Dooley slotted all five of his frees for Tullamore.
On Saturday, Kinnitty beat this year's league champions Belmont 1-12 to 0-12, while St Rynagh's enjoyed a good win against Coolderry - that finished 2-19 to 0-16.
While on Thursday, Ballinamere and Birr played out a 2-17 to 1-20 draw in the championship's opening contest.
Our coverage of the Offaly Senior Hurling championship is with thanks to Leahy Midland Auctioneers.
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