Penalty chances were missed at both ends before Naas got off the mark with a 28th-minute try. The Leinster side had a concerted spell of pressure with their forwards recycling well, the ball was then worked out to the backs and centre Johnny Delaney slipped through the hosts' midfield to score under the posts. David Aherne converted and Naas grew in confidence with that converted try.
Crosshaven, who showed some excellent skills at the breakdown, got some reward for their first half efforts just before the interval when winger Conor Deane was successful with two penalties, the second coming four minutes into injury-time.
Naas, buoyed by three recent wins in the Provincial Towns Cup and the President's Cup, pushed on from 7-6 to 14-6 in front, midway through the second half.
There was no stopping powerful number eight Andrew Melville who picked up off the base of a scrum and muscled over, allowing Aherne to convert from close range.
But Crosshaven never far behind and their attack looking sharp, they managed to immediately strike back with a converted try of their own. Robert Barry, their hard-working number eight, crashed over with Deane converting.
But an Aherne penalty an injury-time try from inside centre Henry Bryce, who showed great power and pace to beat four tacklers and touch down, saw Naas secure an opening day triumph. Aherne's conversion was the last kick of the game, taking his personal tally to nine points.
Ulster Qualifying League champions Armagh, who travel to Naas next weekend, also made a winning start to the Round Robin series.
Willed on by a large crowd at the Palace Grounds, Armagh scored a 23-13 victory over Connacht League winners Monivea. Colin Steenson's Armagh side proved too strong with wily centre Johnny Allen showing glimpses of his best by scoring three tries.
Place-kicker Johnny Steenson converted one of those tries and added two penalties to give the hosts enough of a buffer to see out the win. However, their Galway opponents did have some purple patches, one seeing full-back Kevin Higgins slice through for a converted try.
Monivea host Crosshaven this coming Saturday with a win vital to both sides' chances of becoming an AIB League club for next season.
WEEK ONE - RESULTS:
Crosshaven 13 Naas 24, Myrtleville Cross
Armagh 23 Monivea 13, Palace Grounds
WEEK TWO - FIXTURES:
Saturday, March 31: Naas v Armagh, Monivea v Crosshaven