Mayo 4-16 Galway 0-11
Red cards for both Garreth Bradshaw and Niall Coleman didn't help Galway, but Mayo tore them asunder before that in a comprehensive win at Pearse Stadium.
Cathal Carolan, Enda Varley and Donal Vaughan all hit the net for Mayo in the first-half, but their win was crowned by a goal from the returning Andy Moran in injury-time.
Galway can have no complaints about the manner of their defeat as they never tested James Horan's Mayo, who blitzed them from the off.
By the 11th minute Mayo had opened out a 0-5 to 0-2 advantage, but when Carolan made the most of a slip at the back by Johnny Duane to finish past Mauns Breathnach with a classy goal the writing was on the wall for the home side.
The lively Danny Cummins replied for Galway to pull his side within four points but last year's All-Ireland runners-up powered ahead to the break with 1-4 without reply.
Two of those points arrived from Cillian O'Connor, before Alan Dillon – who was a late inclusion for Darren Coen – again punished poor Galway defending with a well taken point from the right.
But Galway were well and truly buried when Varley rattled the roof of the net four minutes from the break after a slick move which featured Carolan and O'Connor after Tom Flynn was caught in possession.
Once again Cummins hit back with a point for Galway, but the final nail in the coffin was delivered in the 34th minute when Vaughan was handed the easiest of tasks to finish to an empty net after the Galway defence was caught napping once again.
The chances of a Galway win were very slim when they trailed 3-9 to 0-6 at half-time, but they disappeared three minutes after the restart when Bradshaw was sent off following an altercation with Carolan.
Galway responded to the sending off with three points in a row, but when Coleman followed Bradhaw to the sideline in the 51st minute after a clash with Dillon, Mayo knew they could start to play for a semi-final against Roscommon.
Mayo: D Clarke; K Higgins, T Cunniffe, G Cafferkey; L Kegan (0-1), C Boyle, D Vaughan(1-1); A O'Shea, S O'Shea; K McLoughlin, C O'Connor (0-6, 4f), C Carolan (1-0); E Varley (1-3), A Freeman (0-1), A Dillon (0-2).
Subs: S McHale for Cafferkey (half-time), R Feeney (0-1) for Freeman (54 ), D Coen (0-1) for Dillon (58 ), J Burke for Keegan (59 ), A Moran (1-0) for Carolan (61 ), J Gibbons for A O'Shea (68 blood).
Galway: M Breathnach; J Duane, C Forde, G Sweeney; G Bradshaw, K Kelly, G Sice; N Coleman, F Ó Curraoin; T Flynn, P Conroy (0-1), C Doherty; S Armstrong (0-2, 2f), M Meehan (0-5, 4f, 1'45), D Cum (0-2).
Subs: S Walsh (0-1, 1f) for Doherty (23), J Moore for Sweeney (half-time), G O'Donnell for Armstrong (54), E Concannon for Sice (61), M Martin for Meehan (61)
Referee: Marty Duffy (Sligo).