The Irish province secured a bonus point by half-time as Darren Sweetnam, Conor Murray, CJ Stander and Simon Zebo all touched down.
After a further penalty try and Stephen Archer score, Stander notched his second try after the break.
Peter O'Mahony came on for his first game since the World Cup before Gabriele Di Giulio's late reply.
Ireland flanker O'Mahony, who has been out of action since sustaining a serious knee injury in Ireland's win over France last October, received a big ovation from the home crowd as he was introduced with 20 minutes remaining.
Sweetnam notched Munster's opening try in the second minute, with Tyler Bleyendaal adding the extras, and the home side were quickly 14-0 ahead after scrum-half Murray finished off a well-constructed line-out maul.
Stander gathered his own charge down to score Munster's third try under the posts and Zebo then ran on to a Murray chip to clinch the bonus point as Bleyendaal's impeccable kicking stretched the lead to 28-0 by the break.
The penalty try came shortly after the resumption after Sweetnam was tackled without the ball as he looked certain to race in and collect it following a kick in behind the Zebre defence.
Replacement fly-half Keatley's break set up prop Archer's try and, after wing Di Giulio got Zebre off the mark, Stander notched his second touchdown thanks to a slick pass from replacement scrum-half Duncan Williams.
The win maintained Munster's satisfactory start to the season under new director of rugby Rassie Erasmus but they will expect a much tougher test against their Irish provincial rivals Leinster next weekend.
Munster: Zebo; Sweetnam, Earls, Taute, Wootton; Bleyendaal, Murray; Kilcoyne, Casey, Archer; Ryan, O'Shea; Holland (capt), O'Donnell, Stander.
Replacements: N Scannell for Casey 67, Cronin for Kilcoyne 60, Ryan for Archer 67, O'Mahony for O'Shea 60, Oliver for O'Donnell 67, Williams for Murray 60, Keatley for Bleyendaal 48, Bohane for Earls 48.
Zebre: Padovani, Di Guilo, Bisegni, Castello, Venditti, Canna, Palazzani, Lovotti, D'Apice, Chistolini, Geldenhuys, Koegelenberg, Sarto, Meyer, Ruzza
Replacements: Postiglioni for Lovotti 64, Roan for Chistolini 50, Furno for Meyer 65, Engelbrecht for Palazzani 68, Boni for Castello 55, Greeff for Venditti 54.
Not used: Festuccia, Minnie.
Munster made it four wins from their opening five games in the Pro12 as they strolled to victory over Zebre.