Aled Brew scored a wonderful solo try and Jason Tovey scored another 16 points to take his total to 71 in four games, while he extended his successful run of kicks to 24 before he finally failed with a conversion attempt.
All that meant Munster were send packing from Rodney Parade with nothing to show from their trip to Wales, and as a result, they drop out of the Play-Off Zone while the Dragons close in on the leading teams in the League.
Munster are now fifth on the table, with 30 points from 12 matches, while Turner's team sit in sixth, just one point behind.
And the coach was thrilled with how his team performed. He said: "These guys (Munster) have won European Cups, but we showed we can mix it with the best now."
"We were well marshalled at nine and ten, we played some quality football and Aled Brew's try was one of the best tries we'll see in the season.
"I would have taken 4-0 this morning, but being greedy we could have had five. I was a bit disappointed we bombed out a bonus point, but the atmosphere and the support was as good as it's been for a long time.
"We showed a lot of resolve, which is key in these tight games. We pressurised them and didn't let them have a free run, our back three were outstanding and our half-backs were more than a match for them, Tom Willis led really well and Gavin Thomas could easily play for his country now.
"We have owed Munster and we deserved that, it's about time. We have got back on the horse after Christmas and showed we can play some good stuff, but we've got to be more consistent when we are under the pump."
Guinness PRO12
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