Mayo completed a four-in-a-row of Connacht title victories with a comfortable 3-14 to 0-16 victory over Galway at Elverys McHale Park in Castlebar.
The Green and Red dominated the majority of the first-half scoring a 24th minute goal when Cillian O'Connor's clever pass was palmed to the back of the Galway net by Lee Keegan.
Trailing 1-09 to 0-05 at the interval Galway rallied briefly in the third quarter, but a 48th minute Jason Doherty goal was followed by a third major on 56 when Barry Moran finished off a sweeping move.
Ten minutes from the end Shane Walsh, who scored 0-07 for Galway, had a penalty saved by Mayo custodian Rob Hennelly.
The Tribesmen struggled as Mayo completely negated the midfield influence of Galway's Tom Flynn and Fiontan O'Curraoin.
Amazingly, Galway only gathered two of their own 15 kick-outs in the first 35 minutes as Mayo were primed for a battle.
Aidan O'Shea, who started at centre forward, dropped deep to gather plenty of breaking ball which meant Mayo were in the ascendancy.
At the end of the first quarter Mayo, with O'Connor sharp in the corner, led by 0-05 to 0-02 and Galway were in trouble.
Kevin McLoughlin was highly productive for Mayo and added a point before his side struck a 24th minute goal.
Andy Moran and O'Connor combined creating an opportunity for Keegan, who had timed his run to perfection.
Galway's conversion rate up front was poor as they only managed to hit five first-half points from 12 scoring attempts.
O'Connor and McLoughlin remained key figures until the interval as Mayo trotted off protecting a commanding 1-09 to 0-5 advantage.
After the restart Galway reeled off three points in a row from Walsh, Conroy, and Bradshaw to trim the deficit, but Mayo responded.
In the 48th minute Doherty dashed on to a Seamus O'Shea pass to slam a second Mayo goal which edged James Horan's side 2-12 to 0-10 ahead.
Six minutes later O'Connor and Keegan were involved in the build up as Barry Moran palmed an insurance third goal.
Galway were valiant and when Conroy was fouled by Barry Moran, Walsh's subsequent penalty was saved by Hennelly.
Alan Mulholland's Tribesmen fought until the bitter end and they will now face Tipperary in round four of the qualifiers.
Mayo, beaten All Ireland finalists in the last two years, advanced to the quarter final where they will hope to make an impact once again.
Mayo: R Hennelly; C Barrett, G Cafferkey, K Higgins; L Keegan (1-01), C Boyle, D Vaughan; S O’Shea, B Moran (1-00); K McLoughlin (0-03), A O’Shea, J Doherty (1-01); C O’Connor (0-08, 5fs), A Moran, A Dillon (0-01).
Subs: M Conroy for Dillon (44mins), A Freeman for A Moran (53mins), J Gibbons for B Moran (60mins, black card), K Keane for Boyle (69mins), D O’Connor for Doherty (69mins), M Sweeney for A O’Shea (70mins).
Galway: M Breathnach; A Tierney, F Hanley, D O’Neill; G Bradshaw (0-01), G O’Donnell, P Varley; F O’Curraoin, T Flynn; M Lundy (0-01), S Walsh (0-07, 5fs), D Comer; P Conroy (0-04), E Hoare, D Cummins (0-01).
Subs: J Kavanagh for Comer (24mins), D Burke for Tierney (44mins), S Armstrong (0-02) for Cummins (44mins), G Higgins for Hoare (55mins), J O’Brien for Lundy (62mins).
Referee: R Hickey (Clare).