Sinoti Sinoti and Giovanbattista Venditti efforts for the hosts ultimately proved in vain, and their ninth losing bonus point will do little to ease the pain of their 22nd straight league defeat.
Zebre got off to a solid start and within the opening two minutes found themselves ahead when fly-half Daniel Halangahu slotted home a penalty.
The visitors were quick to respond though - wing Murphy showcased some good hands and went over on five minutes. Centre Ian Keatley did the honours with the boot.
But Zebre stood up to the Munstermen and on 14 minutes they found themselves ahead when Sinoti - after a TMO review - was adjudged to have crossed and Halangahu added the extras.
However, four minutes later Zebre were undone after a period of pressure from the Munster scrum allowed No.8 Butler to touch down. Keatley's kick gave Munster a 14-8 lead.
Ill discipline was proving to be the visitors' downfall though and Australian Halangahu, unfazed by the bright sunshine in northern Italy, notched his third kick of the evening before Gonzalo Garcia took over the duties from the tee and levelled the scores at 14-14 with Zebre's third penalty.
And four minutes before the break the hosts retook the lead, Venditti went over in the corner and, despite Halangahu's missed conversion, Garcia added a late penalty for a 22-14 half-time lead.
Within two minutes of the restart Keatley reduced the arrears to five points when he was presented with a three-pointer.
Garcia then failed with a long-range penalty attempt on 47 minutes for Zebre and that miss was made all the more costly when Keatley notched another ten minutes later.
But the hosts' policy of changing kickers paid more dividends when Halangahu took his personal tally to nine points and Zebre's lead to 25-20 just before the hour mark.
Keatley's toughest kick of the evening, around 40 metres out, proved too far out for the former Connacht fly-half but Botha made an immediate impression when he crossed two minutes after coming off the bench.
Keatley had little trouble putting Munster back into the lead with the conversion but Halangahu missed a 73rd-minute penalty that would have seen Zebre take a one-point advantage.
Keatley did the same with two minutes remaining, his effort drifting wide of the posts, which offered Zebre the chance to steal a dramatic victory but they failed to break down a resolute Munster defence.
|Zebre Score Card|
|Munster Rugby Score Card|