After giving away a number of penalties, the referee lost patience and sent Cross Keys skipper Rob Nash to the bin after he kicked the ball out of the hands of opposition scrum-half Duncan Williams.
The act was to prove crucial as Munster put the penalty into the corner for Billy Holland to catch the ball at the tail of the lineout which followed. Williams peeled around the back of it and went through the gap which Nash should have been guarding.
Outside-half Scott Deasy converted to add to his three earlier penalties as Munster finished the half 16-12 ahead, with Jason Tovey banging over four penalties for Cross Keys.
Despite holding the lead on three separate occasions in the first spell, it was clear Cross Keys were hanging on at times and needed to open the scoring in the second half to have a real chance.
However Luke O'Dea streaked over just three minutes after the re-start before Deasy added another penalty to move Munster 14 points clear.
Munster saved their best for last with all-action No. 8 Paddy Butler finishing off a blistering attack.
Munster A (16) 31: Tries: D Williams, O'Dea, Dineen; Cons: Deasy 2; Pens: Deasy 4
Cross Keys (12) 12; Pens: Tovey 4