Monaghan clinched promotion to Division 1 of the Football League with this one-point win over a Galway side who remain in Division 2 despite their defeat.
The Ulster champions led 0-8 to 0-5 at the interval at Clones.
Galway chipped away at Monaghan's lead after the break but the Tribesmen then had keeper Thomas Healy dismissed after a clash with Conor McManus.
Monaghan moved three ahead only for Galway to level in injury-time but Paul Finlay's point sealed the home win.
Dessie Mone, Stephen Gollogly, McManus and Colin Walshe hit four unanswered points for Monaghan early on but Michael Lundy and Cathal Mulryan got Galway off the mark.
Dermot Malone and Dick Clerkin were among Monaghan's other first-half scorers with Sean Armstrong replying with a couple of points at the other end.
In the third quarter, Galway twice cut Monaghan's lead to the minimum but they were unable to get on terms.
Monaghan were leading 0-11 to 0-9 when Galway keeper Healy was dismissed after his apparent tangle with McManus.
A Kieran Hughes point extended Monaghan's lead to three before scores from Adrian Varley, Paul Conroy and Shane Walsh tied up the match as it entered injury-time.
A draw would have been enough to have secured promotion for Malachy O'Rourke's side but Finlay had time to pop up with the winner to ease any Monaghan nerves.
Sunday's Allianz Football League results
Kerry 1-11 2-18 Cork
Kildare 1-22 0-08 Westmeath
Mayo 2-12 1-07 Derry
Tyrone 1-15 3-10 Dublin
Armagh 1-08 2-10 Donegal
Laois 1-16 2-10 Down
Louth 1-12 2-10 Meath
Monaghan 0-13 0-12 Galway
Fermanagh 3-10 2-13 Offaly
Roscommon 0-12 1-06 Sligo
Wexford 1-15 2-10 Longford
Antrim 0-06 0-10 Clare
London 1-07 2-06 Leitrim
Tipperary 0-22 4-12 Wicklow
Waterford 1-09 0-09 Carlow
Division 2A Final
Kerry 3-16 3-13 Carlow
Roscommon 2-14 4-12 Donegal
Tyrone 0-13 1-09 Leitrim