Mark Connolly kicked 11 points - a conversion, two penalties and a drop goal - for the visitors. The talented full-back has now scored a total of 105 points during the league campaign.
The result sent the Cookies into play-off contention with the final round of matches in Division Two taking place next weekend.
Old Belvedere and Greystones are already through to the semi-finals, having guaranteed themselves first and second place in the division and promotion back to the top flight.
But the final two play-off spots are well and truly up for grabs with Old Crescent, Barnhall, Highfield, Dublin University, Young Munster and Clonakilty all still mathematically in contention for inclusion in the final four.
Young Munster should get through, as they are away to bottom side Midleton, who are already relegated, next Saturday.
Dublin University, the team just below them in fifth, face a home clash with Highfield and the students will probably need a bonus point win and other results to go their way to finish in the top four.