Mark Chandler opened the scoring with a penalty on thirty seven minutes for Cobh, but Greg Barry had Mary's level with a penalty on the stroke of half time.
Barry put the Limerick side ahead on fifty two minutes with a second penalty, before Rory Geary got in for a try for Cobh nine minutes from time and Chandler converted for a 10-6 lead.
A minute from time Barry Kelly scored a try for the Limerick side and Barry converted to give the Saints their second win in this competition.
Bandon won the Munster Junior Two League Final at Annacotty with a 20-7 victory over Thomond. Mark Phelan, Olan Crowley and Kevin Lucey scored tries for Bandon and Crowley kicked a conversion and a penalty.
Corca Dhuibhne ended their season with a 13-0 win over Iveragh in the Galwey-Foley Cup Final at Castleisland. Michael Breathnach scored a try for the winners and Shane Griffin converted and also added two penalties.
Munster Junior Cup Final: Clonmel 27, Clanwilliam 9;
Munster Junior Clubs Challenge Cup Final: Cobh Pirates 10, St. Mary's 13;
Munster Junior Plate Final: Tralee 15, St. Mary's 31;
Junior Inteprovincials: Munster 21, Connacht 16;
Ulster 21, Leinster 21;
Munster Junior 2 League Final: Thomond 7, Bandon 20;
Galwey-Foley Cup Final: Corca Duibhne 13, Iveragh 0;