The Faithful will now face Kildare in the quarter finals.
Offaly are one of the eight remaining teams in the Tailteann Cup.
The Faithful saw off the challenge of New York in their preliminary quarter final on a scoreline of 2-25 to 1-12 in Glenisk O'Connor Park on Saturday afternoon.
Dylan Hyland impressed with 1-12, while Ruairi McNamee came off the bench to register their second goal.
Despite the comfortable win Offaly did manage to let New York get a foothold in the game towards the end as they outscored the Faithful 1-5 to 0-7 in the final quarter.
Joint manager Mickey Harte says building up a big lead throughout the game was crucial:
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