A solid foundation of 11 points with the aid of the wind in the first half paved the way for an emphatic win by St Gerald's over their Ballina opponents in Ballyhaunis.
The Castlebar students will now meet great rivals St Colman's of Claremorris in the semi-finals.
Wing-back Patrick Durcan set them on their way with an early point and Ronan Carolan and James Durcan also found the target as St Gerald's dominated all over the field.
Matthew Cullen scored a goal for St Muredach's on 10 minutes but that was their only score in the first period.
Mayo minor Sean Regan clipped a few points off the lead in the second half but St Gerald's, who were always playing at a much higher tempo, sealed an impressive win with further points from Carolan and James Durcan.
Andrew Murphy then added the gloss with St Gerald's goal after substitute Jamie Lydon had his shot saved by the St Muredach's goalkeeper, who rescued his side on more than one occasion.
Scorers – St Gerald's: J Durcan 0-5 (1f), R Carolan 0-4, A Murphy 1-0, P Durcan, M Plunkett 0-2 each, J Lydon, J Gannon, M McHugh, S Conlon 0-1 each. St Muredach's: S Regan 0-5 (4f), M Cullen 1-0.
St Gerald's – D McHale; K Egan, M McHugh, K McNally; P Durcan, M Hall, C Dravins; M Ruane, R Coleman; S Conlon, M Plunkett, J Gannon; R Carolan, A Murphy, J Durcan. Subs: E Regan for Coleman, J Lydon for J Durcan, S Kelly for Dravins, P Ruddy for Gannon, D Gibbons for R Carolan.
St Muredach's – R O'Hora; C Naylor, B Walkin, L Hogan; P McGarry, R Geraghty, P Judge; R Upton, C Bourke; O Kent, S Regan, D Gibbons; S Ruttledge, M Cullen, B Keane. Subs: A Melvin for Hogan, K Treacy for Cullen, F Tully for Gibbons.
Ref – P Geraghty (Swinford).