Munster head coach Johann van Graan was relieved to come away from The Sportsground with the victory on the back of a 'tough 80 minutes'.
Having lost to Ulster last weekend, the Reds bounced back with a 16-10 victory to extend their lead at the top of Conference B, but it proved to be a tough evening for van Graan's men as they held off a spirited late comeback from Connacht.
"It was a tough 80 minutes, we got pinned in the first five minutes in our own 22 and we managed to get out. We went 10-0 up and then they scored that penalty on the stroke of half-time, which I thought gave them a bit of belief," van Graan explained to eir sport.
"We were very calm at half-time then went up 16-3 with a few minutes to go and then they scored that try and we conceded a penalty for a high tackle, which put us in our half. So two good teams that played in difficult conditions."
Paying tribute to their opponents, van Graan added: "It was a real intense game, and we had some really good defensive sets, and some good hits. We played against a team that are just behind us in the pool and you don't go and beat Leinster away from home for nothing so they are a quality outfit and we knew that.
"It is always tough coming to the Sportsground, especially in conditions like this, they were full of confidence. It took us a few minutes to get into the game but we are very happy with the win."