Naas had already accounted for Ulster side Rainey and they took the lead when Joey Moran converted Stuart Pringle's early try.
Breen reduced the deficit and a penalty from Liam Delaney saw the home side take a narrow 8-7 lead into the interval.
Delaney and Moran swopped penalties before Moylan struck for what proved a precious try with Moran landing a penalty to ensure a nail-biting finish.
Elsewhere, there was disappointment for Clonakilty and UCC who both failed in their respective play-off bids for promotion.
Clonakilty came closest, losing 25-15 to Barnhall in Parsonstown but UCC were comprehensively beaten on the cabbage-patch back pitch at Lansdowne Road where the home side emerged 29-6 winners.
The students opened brightly and were six points up thanks to two Jeremy Manning long-range penalties.
Felipe Contepomi opened Lansdowne's account with a penalty and the advantage then swung his side's way when referee Alastair McKay awarded a very harsh penalty try. A second try just before the half time whistle effectively sealed UCC's fate.