Alan Lyons' 66th-minute goal sparked away side Offaly to life as they controlled the closing minutes against Wexford yesterday, tagging on three further unanswered points through Karol Slattery and two Niall McNamee frees, to leave the minimum separating the sides.
But the final whistle saved Wexford's blushes as they ran out victors by 1-14 to 2-10.
Sligo bounced back from their loss to Antrim on the opening weekend with a one-point win over Louth at Markievicz Park.
The Yeatsmen were leading 1-9 to 0-6 at half-time thanks to a goal from Adrian Marren but he was then sent off in the second half.
Goals from Colm Judge and JP Rooney (penalty) reduced the deficit but Sligo hung on for their first win of the campaign by 1-14 to 2-10.
James Sherry plundered a last-minute Fermanagh goal to stun Roscommon, who had looked the better side, at Brewster Park, as the home side won by 2-6 to 0-11.
Ryan Carson scored the first goal just after the break from a rebound after his cheeky lob had hit the crossbar.
Antrim came away from Cavan with all the points thanks to a 2-13 to 1-8 Ulster derby victory at Breffni Park on Saturday night.
A goal from Michael Magill 10 minutes from time sealed victory for Antrim.