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Both sides looked unshakable defensively in the first half, forcing each to settle for just a single penalty in the opening 40 minutes.
The Munster fly-half added a second after the break to edge the home side back in front, while the Aviva Premiership outfit struggled to create opportunities.
Andrew Conway thought that he had a try for Munster before the score was ruled out by a review for a forward pass, but they did find the line a couple of minutes later, with Dave Kilcoyne diving over.
Keatley kicked a drop goal shortly after to leave the hosts 11 points up, ensuring that the Irish side start the campaign with back-to-back wins.