Offaly and Westmeath were beaten, while Laois picked up their first point.
Laois and Westmeath began their National Ladies Football League campaigns over the weekend.
Westmeath suffered a 2-11 to 1-6 defeat away to Donegal in Division Two.
The Lake County's goal came from a penalty from Anna Jones, but it wasn't enough as their opponents outscored them by 1-4 to 0-1 in the final 15 minutes to see it out.
Westmeath welcome Tyrone to the midlands this Sunday.
In Division Three, Stephen Duff's Laois side played out an entertaining 3-13 each draw at home to Fermanagh on Sunday.
Mia Branagan scored two goals on her senior debut, while Emily Lacey impressed with 0-8.
They face Down in round two this weekend.
Meanwhile, Offaly were beaten 1-11 to 1-8 away to Leitrim in Division Four.
Offaly host Kilkenny in round three this Sunday.
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