Munster took advantage of an early red card for Zebre's Pierre Bruno to secure a 28-0 Guinness PRO14 victory at the Stadio Giovanni Mari.
Bruno was banished in the ninth minute for leading with the forearm in tackling Munster back-rower Chris Cloete.
Munster took the lead almost instantly as wing Calvin Nash won a kick and chase and outside-half JJ Hanrahan converted.
Zebre defended well in an attritional battle, but Munster made their extra man count after the break.
Hanrahan converted his own try and then added the extras to a Rory Scannell score.
Darren Sweetnam claimed the bonus-point try seven minutes from time and Hanrahan added his fourth conversion as Munster coasted home.
