The defending champion put on a defensive masterclass at Thomond Park to make it nine wins from nine in the competition.
Leinster held off a bright start from Munster to score through Ed Byrne from its first real attack of note.
Ross Byrne added the extras and split the posts again to make it 10-0 after 22 minutes, with JJ Hanrahan getting Munster on the board shortly before the break.
Hanrahan nailed another penalty early in the second half, but for all its endeavour, Munster could not find a way through a stoic Leinster defence.
Edinburgh, which is second in Conference B, overcame Glasgow 29-19 to keep alive its hopes of winning the 1872 Cup — contested annually between the Scottish rivals — for a third straight year, having lost to the same opponent a week ago.
Darcy Graham scored twice for Edinburgh, which was twice behind after the break because of tries from Scott Cummings and George Horne.
Benetton Treviso made it two wins over Italian rival Zebre in the space of a week, hooker Hame Faiva scored a hat-trick in a 36-25 win despite the early sending off of Juan Ignacio Brex.