Ian Keatley bagged Munster's first try after 90 seconds while Niall Ronan contributed the second 11 minutes later - fly-half Ronan O'Gara converting both.
Replacement Conor Murray grabbed the third after the break then came Zebo's score four minutes later with O'Gara converting the latter but not the former for a 26-6 lead.
Tom Prydie and Lewis Robling had earlier kicked penalties for the Dragons who scored a try of their own through Dan Evans five minutes after Zebo's effort for Munster.
Robling converted but Munster had the final say when Tommy O'Donnell scored and O'Gara slotted home again for a 33-13 win and second in the RaboDirect PRO12 table.
Scarlets have the same three wins and one loss record and sit top courtesy of one extra bonus point but Penney is refusing to get ahead of himself.
"By no means were we perfect and they [the Dragons] breached us a few times," Penney told the official Munster website.
"They made our lads work hard and they presented us with challenges so we certainly weren't perfect.
"Everyone is putting pressure on for a starting spot but it's really about the depth of players we have and it's critical for us to get through the season, guys can't play in every game.
"It is early days and we just have to keep our feet on the ground working on our game again this week."
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