Despite tries from Johne Murphy and Paddy Butler - Murphy almost snatched a second - they trailed 22-14 at half time and again by five points on the hour mark but worked a good try from BJ Botha in the 65th minute that Ian Keatley converted for the vital lead.
They had to survive an onslaught in the final ten minutes and a Daniel Halangahu touchline penalty but ended the game pressing inside the Zebre 22, winning a scrum penalty that was kicked to touch to end what had been a good contest.
Munster: D Hurley; R O’Mahony, C Laulala, I Keatley, J Murphy; JJ Hanrahan, C Sheridan; D Kilcoyne, M Sherry, J Ryan; B Holland, P O’Connell capt; Dave O’Callaghan, S Dougall, P Butler. Replacements: N Scannell, J Cronin, BJ Botha, I Nagle, B Holland, D Williams, C Bohane, F Jones.
Zebre: R Trevisan; G Venditti, A Benettin, G Garcia, S Sinoti; D Halangahu, T Tebaldi; Matias Aguero, D Glazzon, D Ryan; J Sole M Bartolami capt, F Ferrarini, M Bergamasco, A Van Schalkwyk. Replacements: A Manici, L Leibson, A De Marchi, E Caffini, F Cristiano, A Chillon, M Pratichetti, S Pace