The hosts had started the game on the front foot, and following an extended spell of pressure inside the Fintan's half, they forced the Sutton outfit into the concession of a fifth-minute penalty, converted expertly by out-half Darragh Irwin.
This was a vital score for Mount Temple to get early on, as it offered them some much-needed breathing space in the early moments.
Fintan's coped admirably with the Clontarf school's powerful pack for much of the opening period, although a good spell of play did lead to an impressive drop goal from close-range by Irwin on 11 minutes.
Mount Temple now had a platform on which to build, and though Fintan's deserve plenty of credit for the way they managed to force the play into midfield, they were somewhat fortunate when a 27th-minute Irwin penalty came back off the upright and into the waiting arms of Fintan's full-back Nicky Usher.
Mount Temple did finish the half in fine spirits, however, when the outstanding Gibney drove over two minutes into time added on following a line-out in the left corner. Irwin was narrowly off target with his bonus attempt, but his team were now well placed thanks to a 11-0 interval lead.
This left Fintan's with a mountain to climb after the break, but with Joe Dowling and Adam Kidd introduced early in the second half, they started to force their way into the reckoning.
Mount Temple were finding themselves under pressure for the first time in the contest, and their cushion was significantly reduced when hooker Liam Litchfield touched down to the left of the posts for a try that was converted superbly by captain Conor Wickam on 42 minutes.
Mount Temple never allowed panic to seep into their play, though, and Irwin increased his personal tally to nine just moments later from a 30-metre penalty.
This helped to put a sting in the momentum that Fintan's had built up, and with Gibney's strong running consistently causing them problems, Mount Temple managed to regain a stranglehold on the proceedings.
Good work by Gibney did manufacture another penalty for his side after 57 minutes, and Irwin put 10 points between the teams with his successful effort.
This proved to be the last score of the afternoon, and even though Mount Temple went close to conjuring up a second five-pointer in the closing stages, Irwin's second-period penalties were more than enough to get them past the spirited challenge of Fintan's.