The Italian side looked on course to end a disastrous season with a flourish when they went in at the interval 22-14 ahead.
However, Munster, who themselves have an endured a forgettable few months, hit back in the second half and BJ Botha's 65th-minute try, which was converted by Ian Keatley, gave the visitors the points.
Rock-bottom Zebre did at least collect their 10th losing bonus point but it will be scant consolation for the Parma-based outfit.
They made a decent start with fly-half Daniel Halangahu slotting home a penalty in the second minute although the Irish side came storming back when Johne Murphy touched down in the corner, with Keatley adding the extras.
Given Zebre's woeful record, many would have been forgiven for thinking Munster would then run riot at the Stadio XXV Aprile.
However, the hosts bounced back superbly and scored their first try in the 14th minute through Sinoti Sinoti - albeit after the TMO had to adjudge whether Samoan wing had crossed the line.
Halangahu missed with his conversion attempt and Zebre were further undone four minutes later when their defence cracked from some Munster pressure, allowing number eight Paddy Butler to go over from a scrum.
Keatley put the visitors 14-8 ahead but some poor discipline allowed Zebre a route back into the match, with Halangahu and Gonzalo Garcia both adding penalties to level proceedings.
And there proved to be no stopping the Zebre juggernaut as Giovanbattista Venditti touched down in the corner before Garcia notched another penalty to give them a surprise 22-14 lead at the break.
Keatley reduced the deficit to just two points with as many penalties at the start of the second half although Halangahu gave Zebre some breathing room with 20 minutes remaining with his third penalty of the encounter.
Replacement Botha helped Munster retake the lead when he touched down just two minutes after being introduced and Keatley maintained his 100 per cent conversion rate to give Rob Penney's men a two-point lead heading into the final 15 minutes.
Halangahu could not find the target with his penalty seven minutes from time which would have put Zebre back into the lead, while Keatley saw an effort sail wide of the posts in a nail-biting finale.
That gave Zebre one final crack to break down Munster but the visitors' defence held firm to seal a dramatic victory and one that ensured sixth place in the standings.
- Sports & Recreation
- Ian Keatley
- Daniel Halangahu