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A penalty from Paul Burke in the closing stages put an end to Ulster’s resilience at a cold Musgrave Park.
Munster remain 13 points behind the pace-setting Ospreys, who grabbed the maximum against the Dragons on Friday night, with three rounds to play.
Burke opened the scoring in the first few minutes but Ulster soon proved they meant business.
Winger Tommy Bowe brought his side straight back into contention with his seventh try of the season.
A John Kelly try restored Munster’s advantage but a drop goal from Paddy Wallace tied the scores up at 8-8.
Mark McCall’s men took the initiative again with a try from Roger Wilson shortly after the half hour.
But Burke reduced the deficit before David Wallace insured the home side went into the break the better.
Burke’s extras pushed Munster 18-15 in front and their dogged determination, led by captain Jim Williams, was rewarded again late on when Burke kicked what was the winning penalty.