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.
Kilbeggan Races Returns Tomorrow Afternoon
Laois SFC: Graiguecullen And Stradbally Pick Up Opening Round Wins
Offaly SHC: Kilcormac Killoughey Face Kinnitty In Must Win Game
Westmeath SFC: Opening Round Begins With Bang
Athlone Town Advance In Women's Champions League Qualifying Round
Laois SFC: Round One Gets Underway This Evening
Mullingar Harriers Athletes Shine On International Stage
Athlone Town To Face Waterford In FAI Cup Third Round
Athlone Town Cruise To Victory In Women's Premier Division
Offaly SFC: Bracknagh Stage Second Half Comeback To Defeat Durrow
Laois SHC: Drama Unfolds In Round Two
Athlone Town Book Place In FAI Cup Third Round
Westmeath SHC: Castletown Geoghegan Maintain Perfect Record
Offaly Athletics Club Launches €150k Fundraising Drive
Laois Book Place In All-Ireland Intermediate Camogie Final
Alex Dunne Finishes Fourth At Spa-Francorchamps
Offaly SFC: Shamrocks Seal Huge Win Over Edenderry
Ryan Fox Crowned 2026 Open Champion
World Cup: Spain Are World Champions