There was no bonus point to take home to Galway, but there was plenty for Pat Lam to savour as his troops climbed level on points with Saracens, who were beaten at home by Toulouse the night before.
George Naoupu and Mata Fifita scored a try in each half for Connacht, while Dan Parks did the rest, registering 23 points with his trusty right boot.
For Zebre, Luciano Orquera kicked all their points, but they failed to register so much as a losing bonus point on yet another failed adventure for the Italians.
Connacht led this one pretty much from start to finish, a second minute penalty by Parks setting them on their way against the only side they had previously beaten this season.
Zebre came into the game with ambitions of their own, confident of finally securing their first ever win in European competition, but for all their early endeavour, they did not quite have the tools to pick open a stubborn Connacht defence, and relied exclusively on Orquera for points.
The Italian international traded penalties with Parks as both teams continued to feel their way into the game, Connacht being asked to defend more than they might have reckoned on.
James So'oialo, Robbie Henshaw and Danie Poolman were all asked to make try-saving interventions as the home side laid siege to the visitors' line inside the opening quarter.
In attack, Connacht had opportunities of their own. Henshaw at outside centre was an inspiration every time he touched the ball, while scrum half Kieran Marmion was also lively.
At times they were perhaps guilty of over-complicating things, but their persistence eventually paid off on the half hour when big back rower Naoupu touched down for the opening try following some desperately soft defending from Zebre in the lineout.
Standing at two, the Kiwi barely had to get off the ground as Sean Henry's dart flew straight into his hands and he collapsed over the line.
Parks converted and then added two quick-fire penalties, the net result of which saw Connacht go down the tunnel with a useful 19-3 lead.
Into the second half and the visitors were forced to defend for long periods as Zebre tried to launch a comeback. As in the opening 40 minutes, however, the Italians were unable to convert pressure into tries, with Orquera forced to kick penalties rather than conversions.
He split the posts on 48 minutes to reduce the deficit, but it was a short reprieve for Zebre. Connacht started to play a more territorial-based game and waited for the penalties to come.
And when they did, former Scotland out-half Parks was there on each to occasion to push his side further ahead, kicking three penalties in quick succession to leave Connacht coasting at 28-6.
With the bit between their teeth, the westerners then went in search of tries, and got their second from another lineout set piece, replacement Fifita this time the beneficiary.
With more time they might have added a couple more, but in they end they left content that they had done the job they came to do.
Giving his reaction afterwards, the province's head coach Lam said: "The reason it's called a four-try bonus point is because that's what it is, a bonus.
"First and foremost you have to nail the game. There's no point scoring four tries and then losing the game. I'm sure both Toulouse and Saracens would have liked four points as well but they didn't get them either.
"There's no doubt that we went for it at certain stages, but credit to Zebre for holding us out. But overall we're happy.
"That was a very good team performance by us, a very disciplined performance, especially on the back of what happened last week (against Saracens).
"Everyone said well done for running Saracens close, but asked whether we could do it again. So there was a lot of pressure on us to come out here and win, and to do it so convincingly was satisfying."