Monaghan failed to ease their relegation worries as they lost to Galway at the neutral Longford venue.
Full-forward Paul Conroy led the line superbly for Galway who netted a late goal through substitute Danny Cummins.
Monaghan had looked likely winners in the first half and Paul Finlay, Chris McGuinness, Darren Hughes, and Dick Clerkin helped them lead 0-8 to 0-6.
Galway's introduction of Padraig Joyce proved instrumental in swinging the Division Two contest their way.
Monaghan have earned only four points in their six games and they are tied with Meath, Westmeath and Louth.
On the final day, Eamonn McEneaney's men are away to 100% side Tyrone who have been promoted to Division One.