Garryowen scored four tries, the first, by Harry McNulty, on the stroke of halftime, which gave them an interval lead of 11-6.
But in the second half the visitors took control and led 30-16 by the time Sean Rennisson had a Young Munster try which Willie Staunton converted to add to his two penalties and drop goal.
That raised hopes of a losing bonus point but Jamie Gavin kicked a late penalty to earn the bragging rights. He kicked two earlier penalties and converted two of the tries with Niall Cronin, Mark Rowley and James McInerney all touching down in the second half.
UL Bohemian 39, Malone 34.
UL Bohemian won a sparkling contest on the 4G artificial surface at UL which produced a nine try thriller.
Rory Cunningham (2), Rory White, John Sutton and Kevin Flanagan touched down for the home side with Rory Bourke converting four of the five and he also kicked two penalties.
Neil Arnold scored a brace of tries for the visitors with Mark Gribbon and Conor Joyce also touching down. James McKinney converted four of the tries and also kicked a penalty.
In Division 2A U.C.C. kept their promotion hopes alive with a 47-3 win over Old Crescent at the Mardyke, a result that leaves the Limerick side still in relegation trouble. The students led 21-3 at half time and had tries from Cian O'Halloran (2), Ned Hodson, Brian Vaughan, Conor Barry, Tom O'Hare and Joe Holland. Sean Og Murphy kicked six conversions and Cathal Monaghan replied with a penalty for the Rosbrien side.
Cashel caused an upset with an 18-14 home win over promotion chasing NUIM Barnhall at the Spafield.
Highfield fought back from being 14-5 down at half time to earn a losing bonus after going down to a 171-2 home defeat by Banbridge, Ben Murphy and Kevin Foyle scored tries for the 'Field and Ian O'Donoghue kicked a conversion.
In the big game in Division 2B leaders Nenagh Ormond maintained their unbeaten record with a narrow 16-15 away win over Thomond.
Nigel Daly scored a try for Nenagh, Donal Fogarty converted and also added two penalties and John Lillis kicked one. Dermot Fitzgerald replied with five penalties for Thomond.
There was mixed fortunes for the two Cork sides in this Division 2B. Midleton travelled to Drogheda and defeated Boyne 22-20 to ease their relegation worries and Sunday's Well lost 54-17 away to Skerries. Shane Desmond, Roderick McDonald and Paddy Hughes scored tries for the 'Well and Shane O'Riordan kicked a conversion.
Richmond moved up to the top half of the table with a 14-6 away to Sligo.
Ulster Bank League Division 1A: Ballynahinch v Old Belvedere postponed;
Cork Constitution 6, Dolphin 9;
Lansdowne v St. Mary's College postponed;
U.C.D. v Clontarf postponed;
Young Munster 16, Garryowen 33;
Division 1B: Buccaneers 20, Dublin University 17;
Dungannon v Shannon postponed;
Galway Corinthians 29, Blackrock College 12;
Terenure College 24, Belfast Harlequins 7;
U.L. Bohemian 39, Malone 34;
Division 2A: Ballymena 8, Bective Rangers 3;
Cashel 18, N.U.I.M. Barnhall 14;
Galwegians 44, Naas 17;
Highfield 12, Banbridge 19;
Old Wesley 24, City of Derry 25;
Queens University 21, Rainey Old Boys 23;
Seapoint v Bruff postponed;
U.C.C. 47, Old Crescent 3;
Division 2B: Boyne 20, Midleton 22;
City of Armagh 8, Suttonians 5;
Greystones 27, Ards 3;
Instonians 8, Tullamore 14;
Navan 13, D.L.S.P. 3;
Skerries 54, Sunday's Well 17;
Sligo 6, Richmond 14;
Thomond 15, Nenagh Ormond 16;