Man-of-the-match, Gareth Harkin, gave Harps the lead on ten minutes and Damien McNulty added a second on 38 mins.
It was 3-0 on 58 minutes when Kevin McHugh bundled the ball home after Packie Mailey headed a Harkin corner against the bar.
McHugh scored his second and Harps' fourth on 64 minutes. Harkin was hauled down in the area by Avondale keeper, Danny O'Leary who was shown a straight red card. McHugh beat substitute keeper, David O'Keefe, from the resulting penalty.
With the tie over as a contest, Avondale striker, Roy Long, scored on 85 minutes.
Harps now join Derry City St Pats and Shamrock Rovers in the semi final draw.
After the game Diarmaid Doherty spoke with the Harps boss Ollie Horgan