The hosts secured a bonus point win in Limerick to end a run of defeats against their interpro rivals.
Munster secured a bonus-point win over Connacht at Thomond Park on Saturday night to make a good start to the 10-game block of fixtures.
Calvin Nash, Roman Salanoa, John Ryan and Niall Scannell were the Munster try-scorers with Joey Carbery kicking two conversions.
The scoreline was 10-all at half-time but Munster were well on top after the break to move 24-10 in front before a late Connacht try kept the game alive but Munster managed the finish minutes well.
Connacht took the lead when Jack Carthy fired over a penalty after nine minutes. Munster got off the mark when Craig Casey set Nash free in the corner. Byron Ralston then intercepted a Mike Haley pass in the Munster 22 as the visitors retook the lead.
Salanoa brought the teams level as he dotted with the final score of the half. Munster did take the lead on 59 minutes, Ryan powering over from close range. Scannell secured the bonus point win for Munster with Kieran Marmion’s late score only a consolation.
Graham Rowntree’s men are in Edinburgh this Friday for round nine of the URC.