Two penalties from Brian Haugh saw them tail 7-6 at the interval. Haugh put the Limerick side in front on 56 minutes with a penalty and a try by Colin Liston eight minutes later converted by Haugh made it 16-7.
Johnny Holland secured a losing bonus point for Con' with a penalty two minutes from time.
Dolphin lost at home to Old Belvedere 22-10.
The home side hardly saw the ball in the opening quarter as Belvo' raced into a 12-0 lead. However they were a different side for the next twenty and were unfortunate not to be behind at the interval as tries from Darren Sweetnam and John Quill both unconverted saw them trail 12-10. They continued to look for a score in the opening stages of the second half but it all went wrong in the 48th minute. After several drives by the pack at the Belvo' line, Barry Keeshan's drop goal attempt was blocked down and the visitors booted the ball down field to score their third try.
Garryowen are still searching for their first win of the campaign as they lost at home to St. Mary's College 24-15.
Garryowen led twice in the first half but by halftime they trailed 9-14 and despite being reduced to thirteen at one stage in the second half the Dubliners always looked in command.
For their part St Mary's will be disappointed that they could not manage a fourth try.
Jamie Gavin had Garryowen in front with a penalty after twelve minutes but they fell behind when they "bought" a dummy which saw Darren Hudson score the opening try which Gavin Dunne converted.
Garryowen's defence slipped again a few minutes later when again Hudson touched down and Dunne added the points. In between the tries Gavin kicked two penalties for Garryowen.
A few minutes into the second half Gavin landed his fourth penalty to leave only two points between them but a penalty by Dunne was a boost for St Mary's.
They wrapped up the points when skipper Darragh Fanning raced over after a great break by Dunne who kicked his third conversion.
Twenty minutes from the end Gavin kicked a fifth penalty for Garryowen who face the prospect of losing their top grade status for the first time since the competition began.
U.L. Bohemian moved up to third place in Division 1B, two points behind Corinthians after their 24-21 away win over Blackrock College at Stradbrook.
The home side led 14-5 at half time with Eoin Sweeney scoring Bohes try.
Second half tries from Sweeney, John Sutton and Sam Sterling secured the bonus point victory and David Johnston kicked two conversions.
Ulster Bank League Division 1A: Clontarf 16, Lansdowne 13;
Cork Constitution 10, Young Munster 16;
Dolphin 10, Old Belvedere 22;
Garryowen 15, St. Mary's College 24;
U.C.D. 26, Ballynahinch 32;
Division 1B: Blackrock College 21, U.L. Bohemian 24;
Dungannon 3, Belfast Harlequins 13;
Galway Corinthians 10, Malone 3;
Division 2A: Banbridge 7, Galwegians 11;