Laois had to settle for a draw against Colm O'Rourke's Meath.
Westmeath registered a first win under Dessie Dolan in their second round game in the O'Byrne Cup on Saturday.
Last year's Tailteann Cup winners ran out comfortable winners against Wexford, 1-16 to 0-6.
Laois played out an entertaining draw against Meath, 2-10 to 0-16.
And Offaly and Liam Kearns begun their partnership with a 1-9 to 0-7 victory in their O'Byrne Cup first tround contest with Wicklow.