Tadgh Bennett had a 31st minute penalty for Shannon with Robbie Bourke doing likewise for the visitors.
The only try of the game which was scored by Greg O'Shea for Shannon after a defensive clearance was blocked down.
Bennett converted to make it 10-3 at the interval. Bennett, one, and Bourke 2, landed second half penalties.
Ulster Bank League Division 1A: Clontarf 25, U.C.D. 16;
Dolphin 14, Cork Constitution 9;
Garryowen 8, Young Munster 9;
Old Belvedere 30, Ballynahinch 26;
St. Mary's College 28, Lansdowne 33;
Division 1B: Blackrock College 21, Dungannon 32;
Dublin University 17, Terenure College 26;
Galway Corinthians 19, Buccaneers 18;
Malone 15, Belfast Harlequins 25;
Shannon 13, U.L. Bohemian 9;