Galway had to play the entire second half with 14 men but did more than enough to carve out victory when they confined Monaghan to just two pointed frees from goalkeeper Rory Beggan in that period.
The sides were level six times in the opening half but Monaghan, backed by the breeze, went in leading by 0-08 to 0-07 at the interval.
However, their failure to score from play in the second half, along with shooting eight wides, proved costly as Galway took control to carve out their second win of the campaign.
Galway were reduced to 14 men just before the interval when Peter Cooke, after being held down by Monaghan's Michael Bannigan, retaliated and was sent off by Cork referee Conor Lane.
The sides exchanged points three times in the opening quarter with Sean Jones getting Monaghan’s opening two points as Paul Conroy and Matthew Tierney hit the target for Galway with frees from opposite sides.
Tierney landed a good effort from play after Conor McCarthy struck a free for Monaghan before goalkeeper Rory Beggan delivered a trademark free from distance.
Conroy levelled with an excellent effort before a free from him and one from Rob Finnerty put them 0-06 to 0-04 in front after 29 minutes.
Monaghan, who kept lots of men behind the ball and surged forward, got back on level terms through Cillian Lavelle and Dessie Ward before Cooke edged the Tribesmen back in front with an excellent score.
It was his last action. Bannigan equalised before his tangle with Cooke and then Beggan edged them in front with the free which resulted from the dismissal.
Beggan doubled the lead two minutes after the restart but Galway, after introducing Shane Walsh for his first action for the county in 2023, hit back with three points in a row from John Daly, Sean Kelly and Johnny Heaney, the latter two coming from good goal chances.
Another Beggan free was followed by two excellent points from Finnerty before Cathal Sweeney set up Johnny Heaney for a goal seven minutes from time after Monaghan failed to deal with a high free from Conroy and there was no way back from there for Vinnie Corey’s men after that.
Galway: Connor Gleeson, Johnny McGrath, Eoghan Kelly, Sean Kelly; Dylan McHugh, John Daly, Daniel O’Flaherty; Paul Conroy, Matthew Tierney; Paul Kelly, Peter Cooke, Cathal Sweeney; Rob Finnerty, Patrick Kelly, Johnny Heaney. Subs: Shane Walsh for Patrick Kelly (42), John Maher for O’Flaherty (64), Cian Hernon for Sweeney (71)
Monaghan: Rory Beggan; Thomas McPhillips, Kieran Duffy, Ryan Wylie; Conor Boyle, Dessie Ward, Ryan O’Toole; Darren Hughes, Cillian Lavelle; Stephen O’Hanlon, Michael Bannigan, Conor McCarthy; Sean Jones, Karl Gallagher, Fintan Kelly. Subs: Shane Carey for Kelly (half-time), Conor McManus for Jones (47), Kieran Hughes for Gallagher (65)
Referee: Conor Lane (Cork)
