Ronan O'Mahony and James Cronin both notched two tries with Tommy O'Donnell and the Scannell brothers Niall and Rory also touching down for Munster.
Derick Minnie scored a first-half try for Zebre as Munster led 24-7 at the break with Lloyd Greeff also scoring for the Pro12's bottom club in Parma.
The Italian club have lost 16 of their 17 Pro12 matches this season.
Ireland hooker Niall Scannell finished off a maul to open Munster's account in the third minute before his fellow international O'Donnell extended the lead on 18 minutes.
After wing O'Mahony's first try, Minnie replied for Zebre on the half-hour mark before a Tyler Bleyendaal penalty left Munster 17 points clear at half-time.
Munster centre Scannell joined his older brother on the scoreboard with the first try of the second half to ensure his side a bonus point, before O'Mahony secured his brace after Marcello Violi was sin-binned for the hosts.
Despite their numerical disadvantage, Zebre reduced the deficit to 12 points through a converted try from South African Greeff with just under 25 minutes to play.
But Munster quickly reasserted their authority as prop Cronin marked his comeback from injury with two tries in the final 20 minutes, both converted by Rory Scannell.
Zebre: D Berryman; K Van Zyl, T Boni, T Castello, L Greeff; S Bordoli, M Violi; B Postiglioni, O Fabiana, B Le Roux; G Koegelenberg, V Bernabo (capt); M Mbanda, J Meyer, D Minnie.
Replacements: S Tobias, A De Marchi, G Roan, J Furno, F Ruzza, C Engelbrecht, M Pratichetti, G Palazzani.
Munster: A Conway; D Sweetnam, J Taute, R Scannell, R O'Mahony; T Bleyendaal, D Williams; D Kilcoyne, N Scannell, J Ryan; D O'Callaghan, B Holland (capt); P O'Mahony, T O'Donnell, J O'Donoghue.
Replacements: R Marshall, J Cronin, S Archer, D O'Shea, C Oliver, A Lloyd, D Johnston, D Goggin.

The CPS said there was "insufficient evidence to provide a realistic prospect of a conviction against the arresting officers".
One officer, Paul White, will face trial for perjury over the evidence he gave at Mr Rigg's inquest.
Mr Rigg died at Brixton police station in 2008.
The inquest into his death in 2012 found police used "unsuitable" force when they arrested Mr Rigg.
In a statement, the Metropolitan Police Service said it "welcomes today's decision" and "would again like to emphasis its sympathy to Mr Rigg's family".
But Marcia Rigg, Sean Rigg's sister, said she "had hoped for an opportunity to get justice".
The family's solicitor Daniel Machover said the family would "urgently consider reviewing" the decision under the Victims' Right of Review scheme.
"There are some serious concerns about the legal basis of the CPS decision today," he said.
Munster continued their march towards the Pro12 play-offs as they earned a 50-14 bonus-point away win over Zebre.
[NEXT_CONCEPT]
The Crown Prosecution Service (CPS) has said it will not prosecute five police officers over the death in custody of Sean Rigg in 2008.