Jonathan Ruru extended Cashel's advantage with a second try, but Dolphin hit back with a try from Chris Rowe and Barry Keeshan converted to leave it 13-7 at half time
Cashel continued to dominate after the break and tries by Patrick Fitzgerald, John Ed-O'Connor and Ed Leamy and two conversions by Pat O'Connor saw the Tipperary side advance to a home semi final meeting with Midleton next Saturday.
In the other quarter final tie at Musgrave Park on Thursday evening Cork Constitution defeated Sunday's Well 50-0. Luke Cahill, Garret O'Suilleabhain, Darragh Lyons, Andrew Cudmore, Conor Desmond, Graeme Lawlor and Pat Parfrey scored tries for the winners and Lyons kicked five conversions.
Holders U.L. Bohemian booked their place in the semi finals of the Limerick Charity Cup with a 21-16 win over Bruff at Annacotty.
Rory Whyte scored two tries for the winners and also added a conversion. Darragh Frawley kicked two penalties and Derek Farrell added one. Brian Cahill replied with a try, conversion and three penalties for Bruff.
Old Crescent proved too strong for Thomond at Rosbrien advancing to the semi final on a 36-6 scoreline.
The winners led 10-6 at half time. Alan Bennie scored two tries for the Division 2A side and Larry Hanly, Graham O'Keeffe and Luke Russell got one each. Shane Mullally converted four of the tries and also added a penalty.
Dermot Fitzgerald replied with two penalties for Thomond.
Cork Charity Cup: Cashel 32, Dolphin 7;
Sunday's Well 0, Cork Constitution 50;
Limerick Charity Cup: Old Crescent 36, Thomond 6;
Shannon v Nenagh Ormond postponed;
U.L. Bohemian 21, Bruff 16.