Clare have suffered their second loss of the 2016 Allianz National Football League campaign.
A point deep in injury time saw Offaly take a 0-15 to 1-11 win, just moments after Eoin Cleary had struck for a late goal to level the game.
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The result means the Banner are second in the league standings with two rounds to play, after Sligo beat Kildare and Longford got the better of Tipperary.
Manager Colm Collins says they knew Offaly would not be an easy prospect.
