Galway managed only two points in the last 23 minutes as Mayo stayed in touch through Damien McGing’s accuracy from dead balls.
Galway, who featured a number of Kevin Walsh’s extended squad, including the excellent Enda Tierney at midfield, would have been disappointed to go in level at the break after they held a 0-6 to 0-2 lead after 16 minutes.
Mayo had taken an early lead, a fine point from Farrell on the turn after seven minutes gave them a 0-2 to 0-1 advantage, but with Peter Cooke becoming an increasing influence at centre-forward for Galway the Tribesmen took control.
Cooke drilled over a free to level matters in the tenth minute and straight from the kickout Galway pulled clear when Richard Fahy pointed after he gathered the break.
Cooke was on the mark once again with another well-struck free, before Paul Whelehan and Matthew Reddington chipped in for the Tribesmen.
It looked as if Mayo would be blown away at that stage, but after Darren Durcan pointed, Farrell struck the game’s vital goal when he gathered the rebound of Eoin O’Donoghue’s strike which crashed back off the crossbar.
That goal came as Mayo experienced their best period of the game, as they went from four points behind to three points up in the space of seven minutes.
But with Cooke, Whelehan and Tierney all on target Galway were relieved to go in all-square at the interval.
Tierney was in driving form from midfield and landed Galway’s first two points of the second-half to give the Tribesmen the lead, but from that juncture Mayo bossed the encounter.
A ‘45’ from Farrell and a free from McGing gave Mayo a slight advantage but further scores from Sean Gaughan and Darragh Joyce saw them open out a four-point lead with nine minutes remaining.
Peadar Einne Seoighe and Whelehan kicked scores to give Galway a chance of clawing back that lead, but once Whelehan rattled the crossbar late on Galway’s chance was gone.
A Farrell 1-2 (1 ‘45’), D McGing 0-4 (4 frees), D McHugh, M Forde (free), D Durcan, D Joyce, C Horan, S Gaughan 0-1 each.
P Whelehan 0-4 (2 frees), P Cooke (frees), E Tierney 0-3 each, P E Seoighe, M Reddington, R Fahy 0-1 each.
B Forkan; P Barrett, B Moran, B Leonard; E O’Donoghue, D McHugh, M Barrett; P Collins, P Feerick; D Durcan, B Carr, G Conway; D Joyce, A Farrell, D McGing,
S Gaughan for Conway (23), C Horan for Barrett (29), A Gallagher for Durcan (36), M Forde for McGing (42), J Keane for O’Donoghue (55), K Newell for Horan (60).
M Dolan; A Claffey, A Kyne, C Ó Domhnaill; P E Seoighe, J Shaughnessy, J Heaney; E Tierney, E Commins; M Redington, P Cooke, R Fahy; C Kennedy, P Whelehan, A Hernon.
M Day for Ó Domhnaill (23), N Walsh for Fahy (h-t), F Cooney for Reddington (39), M Fox for Kennedy (50), T Mullins for Commins (53).
Paul Daly (Roscommon).