South African back rower CJ Stander crossed for two second half tries, but Munster head coach Rob Penney will not have been impressed with a sloppy opening half and the concessions of an audacious try by Luciano Orquera.
Despite trailing 18-9 at half-time against a team that has yet to win a league game, Munster recovered well after the restart and Stander's brace allied to further tries from Paddy Butler and replacement Ian Keatley got their Italian expedition off to a winning start.
JJ Hanrahan, who started at out-half, also produced a superb kicking display as he finished with 21 points from five successful penalties and three conversions and was deservedly named man-of-the-match.
The opening half proved a huge disappointment for the province, Zebre's two tries being very well executed but utterly avoidable from Munster's defensive point of view.
The game had started very well for Penney's side who took the lead after five minutes when former Ireland Under-20 star Hanrahan slotted a penalty.
The Kerryman doubled Munster's advantage 10 minutes later after a powerful Munster shove at a scrum on halfway, but by the 22nd minute they were on the back foot as Orquera crossed for a try in bizarre circumstances.
The Munster pack were penalised for failing to roll away from the tackle inside their 22 and after appearing to assume Orquera was going for the posts, the defence switched off.
But the wily out-half, who just minutes earlier had converted a penalty, spotted a gap and just made it across the try-line after a quick tap penalty. The leaking of that unconverted effort leave an embarrassed Munster 8-6 behind.
Hanrahan edged the men in red back in front from the kicking tee in the 32nd minute. The penalty was awarded for a tip tackle on Andrew Conway, with the guilty party - Fijian centre Kameli Ratuvou - earning ten minutes in the sin-bin.
However, the Italians lifted their game while down to 14 men and they dominated up to half-time. Orquera kicked a 36th minute penalty before hooker Andrew Manici scored a terrific try for the hosts.
He slalomed his way through from a left-sided position in the 22, showing impressive pace and evasion skills for a front rower. Munster's missed tackles will have annoyed the management team, with Orquera's conversion putting nine points between the sies.
But thankfully for Munster, they turned in an altogether better performance in the closing 40 minutes as Penney's charges ran in four tries to claim a secon bonus point in six days.
It was a 45th minute penalty from Hanrahan that settled Munster and brought them to within six points of Zebre.
Moments later, a terrific attack from deep saw Johne Murphy split the home defence. The winger hurtled over halfway and linked with the supporting Denis Hurley who passed for young back rower Butler to finish off Munster's first try of the night. Hanrahan's conversion put Munster back in front at 19-18.
At this stage Munster began to gain the upper hand and after forcing a penalty at the breakdown, Hanrahan pushed his side into a four-point lead soon after.
Just short of the hour mark Stander claimed the first of his two tries. Tommy O'Donnell was hauled down near the posts before half-backs Cathal Sheridan and Hanrahan passed right for Stander to crash over for a score confirmed by television match official Alan Falzone.
Orquera kept Zebre within touching distance with a 64th minute penalty to close the gap, yet Munster banished any thoughts of a nervy finish.
Sheridan and Stander combined neatly for the latter's second try, the scrum half sniping through at close quarters before getting the ball free for Stander to finish under the posts.
Keatley then swatted away two defenders close to the Zebre whitewash to make it two tries in nine minutes, converting his own try to complete the comeback triumph.