A Duncan Williams try gave the hosts an early lead before Sam Davies hit back for the visitors but Francis Saili and Robin Copeland crossed either side of the break to put Munster firmly in charge.
However, Owen Watkin came off the bench to pull a try back and the boot of fly-half Davies saw them take home all the points in a tightly-fought affair.
"It's a very pleasing night, in terms of performance and outcome," admitted Rees post-match.
"It was a strong team effort and by that, I'm talking about the entire 23. We used the full number and the bench made a huge impact, contributing fully to the win.
"We built on the second half of the Glasgow game, which in many ways was something of a watershed moment for us. We moved the ball well, we challenged them defensively throughout the game, asking questions, and we got our reward.
"The turnover rate was far too high, we need to get that down as on another day it would have cost us more dearly. They scored 14 points when we were in possession and not really in any kind of danger."
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