Young Munster's will now have a battle on their hands to finish in the top four.
The visitors played with wind advantage and hit the front with a penalty from Shane O'Leary after four minutes but Barry Keeshan had Dolphin level after fourteen minutes.
A try by Darren Gallagher on forty minutes converted by O'Leary restored Young Munster's advantage but Keeshan landed his second penalty on the stroke of half time to leave it 10-6 at the break.
Penalties by Keeshan on 47 and 52 minutes put Dolphin in front. James Kiernan ran in a try three minutes later and Keeshan's conversion came back off the upright.
Keeshan made amends with penalties on sixty and seventy two minutes to secure the points for the home side.
Dolphin: Eamon Mills; James Kiernan, John Gleeson, Chris Bannon, Garrett O'Suilleabhain; Barry Keeshan, Brian Slater; John Leahy, Niall Scannell (captain), Christy Condon; Dave O'Mahoney, Darren O'Shea; Rob O'Herlihy, Miah Cronin, Brian O'Callaghan. Replacements: Will Foley, James Cronin, Chris Roe, Paul Hurley, Cian Bohane
Young Munster: Craig O'Hanlon; Dom Lespierre, Mark Doyle, Lukas Kuntz, Darragh O'Neill; Shane O'Leary, Mike Prendergast; Ger Flaherty, Ger Slattery, Alan Cotter; Sean Duggan, Darren Gallagher; Colin Liston, Mark Rowley, Neville Melbourne. Replacements: Daniel Montgomery, Hugh McGrath, Jack Considine, Tom Goggin, Harry McNulty.
Referee: Mark Patton (IRFU)