Con went into an early lead with two Pat McCarthy penalties before Tom Cregan opened the visitor's account with a penalty and that was followed by a Brian Touhy try to give the Limerick side the lead.
Tomas O'Leary restored Con's advantage with a try but McCarthy missed that conversion and a subsequent penalty before a Mossie Lawlor try and another Cregan penalty had the Shannonsiders 15-11 up at the break.
However, just three minutes after the restart Healy struck for a well worked try and O'Leary score his second before O'Connor sealed the visitor's fate.
Munster squad member Lawlor scored his second try and Cregan converted but it was score that served only as a consolation.
Ballymena 15-0 DungannonBlackrock 25-34 GarryowenBuccaneers 32-14 LansdowneCo Carlow 28-32 GalwegiansSt Mary's College 14-6 UCD.Clontarf 15-32 Belfast Harlequins
AIB League Division Two. Ballynahinch 28-12 Malone Bective Rangers 13-16 D.L.S.P. Midleton 10-18 Old Crescent Old Belvedere 16-5 Barnhall Sunday's Well 16-10 Waterpark Terenure College 11-16 Dublin University
AIB League Division Three. Ards 22-11 Portadown Ballina 38-6 Naas Suttonians 20-18 Clonakilty Greystones 39-5 Instonians Highfield 25-20 City of Derry Skerries 18-16 Wanderers Connemara 6-6 Corinthians Queens University 61-3 Old Wesley