The score opened the floodgates and wingers Sarah Barrett and Jolee Gregory soon added further tries. Newly promoted scrum half Amberley Ruck, in only her second game for the senior side since graduating from the U18 section in December, then scored her second try for the ladies side and Quins led 22-0 at half time.
The Phoenix came out with a new found determination after half time and constant pressure led to a try for prop Alana Shakespeare which was dually converted by Jade Mullen.
The score was a brief respite though as Quins then scored another four tries to pull clear. Captain and emergency fly half Becky Newton added a brace and Evans and Ruck crossed for their second tries later on in the half. Newton, normally a back row forward, converted two of the tries.
Quins Coach Nigel Francis was pleased with the victory. "We do not take any side for granted. Pencoed were strong up front today, they dominated our scrum and looked dangerous from set piece," he said.
"The new cup competition has been a target for us since finishing second in the league behind Neath," added captain Newton.
"It's also a great opportunity for our wider squad players, who have had limited game time, to give the coaches a chance to see what they can do.
"With players away on international duty for most of the remainder of the season, these players will be crucial in our cup campaign.
"Pencoed challenged us in lot areas today and we are looking forward to another tough game in the return fixture."