Con' led 6-5 at half time with two penalties from Johnny Holland sandwiched between a try for Garryowen by Barry O'Mahony.
A penalty and a conversion of a try by Harry McNulty from Jamie Gavin put the visitors into a 15-6 lead after forty eight minutes. Con' rallied and a try by James Ryan converted by Holland closed the gap to two, until Bryan Cagney won it for the home side with a try a minute from time.
Young Munster lost at home to Old belvedere 13-10. The visitors led at half time 3-0 but tries from Ger Slattery and Derry O'Connor were not enough for Munsters to claim victory.
Dolphin were well beaten by leaders UCD at Belfield. The students playing with a strong wind in the first half led 5-0 but the visitors were unable to make use of the elements in the second half. Rory Scannell scored Dolphin's try and Barry Keeshan converted.
U. L. Bohemian defeated bottom side Dublin University 16-13 to keep their challenge alive in Division 1B. The sides were level 3-3 at half time. Jack O'Donoghue scored a try for Bohemian and Robert Bourke converted and added three penalties.
Shannon lost away to joint leaders Buccaneers 25-22. The Limerick side led 11-10 at half time. Richie Mullane and Keith White scored tries for Shannon and Tadhg Bennett kicked four penalties.
In Division 2A U.C.C. kept their promotion hopes alive with a 23-20 away win over Banbridge.
In the Munster derby at Woodleigh Park Cashel defeated Highfield 16-5. Gavin McGrath and Darragh O'Brien scored tries for Cashel and O'Brien added two penalties. Dave Kelly replied with a try for the home side.
Old Crescent lost away to NUIM Barnhall 15-0.
Nenagh Ormond remain top of Division 2B after their 31-3 away win over Tullamore on Friday night.
Thomond shared the spoils with Sligo after they played a 19-19 draw away to Sligo.
DLSP won their first game of the campaign with a 13-7 home win over Midleton
Sunday's Well are still looking for their first win after their 10-9 defeat at home by Ards. Shane O'Riordan kicked three penalties for the home side.
Ulster Bank League Division 1A: Ballynahinch 14, Lansdowne 21;
Clontarf 24, St. Mary's College 13;
Cork Constitution 18, Garryowen 15;
U.C.D. 22, Dolphin 7;
Young Munster 10, Old Belvedere 13;
Division 1B: Belfast Harlequins 18, Blackrock College 6;
Buccaneers 25, Shannon 22;
Dungannon 16, Galway Corinthians 24;
Terenure College 27, Malone 10;
U.L. Bohemian 16, Dublin University 13;
Division 2A: Ballymena 21, Old Wesley 6;
Banbridge 20, U.C.C. 23;
Bective Rangers 28, City of Derry 28;
Galwegians 28, Queens University 0;
Highfield 5, Cashel 16;
N.U.I.M. Barnhall 15, Old Crescent 0;
Naas 17, Seapoint 17;
Rainey Old Boys 10, Bruff 9;
Division 2B: D.L.S.P. 13, Midleton 7;
Instonians 10, Greystones 11;
Richmond 6, City of Armagh 0;
Sligo 19, Thomond 19;
Skerries 32, Boyne 10;
Sunday's Well 9, Ards 10;
Suttonians 19, Navan 24;
Tullamore 3, Nenagh Ormond 31;