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The Welsh side recovered from their 48-20 hammering at the hands of Glasgow last time out, as South African centre Percy Montgomery notched 11 points, with his third of three penalties robbing Munster of a bonus point on 69 minutes.
The Dragons could have gone in front in the 10th minute when out-half Craig Warlow chipped forward after a wayward Munster lineout, but he half was guilty of a knock-on 10 metres short of the home line.
Montgomery went wide with a 15th minute penalty right on the Munster 22, after Munster had pulled down former Wales Under-21 player Peter Sidoli in the line.
Shannon left wing Mossie Lawler failed to get hold of a 25-metre penalty on 25 minutes, but opened Munster’s account two minutes later after Dragons prevented Munster captain Jim Williams from releasing under their posts.
A second was added on 33 minutes for a 6-0 lead, with Dragons’ tight head Chris Anthony sin-binned.
The visitors saw number eight Bobby Skinstad, making his second start, take a quick tap on 38 minutes when a certain shot at the posts was on.
Their attacking guile was rewarded a minute into injury time as Munster scrum-half Frankie Murphy was intercepted by Montgomery in the Dragons’ half, and Warlow’s half break created the overlap for Marinos to glide under the Munster posts.
Montgomery converted for a 7-6 half-time lead for the visitors.
Lawler pushed his 48th minute penalty chance right and wide, and Montgomery punished him fully with his first penalty success on 54 minutes.
Warlow tired a drop goal nearing the hour mark, and with play brought back by Scottish referee Graeme Hannah for a Munster infringement Montgomery stretched the Dragons’ lead to seven points.
Centre Jason Holland moved to out-half for Munster for the final 20 minutes but it made no difference as Montgomery, who turns 30 on Monday, hit over another penalty from 35 metres to condemn Munster to a fourth straight loss.