Blaine Scully and Matthew Morgan got the Blues on top at the break after Guglielmo Palazzani's close-range try give Zebre the lead in a lively first half.
And despite Tom James' effort early after the interval, Giulio Bisegni and Giovanbattista Venditti made Wilson sweat for the final few minutes, dotting down to threaten a famous comeback.
But Cardiff hung on and Wilson believes being able to win in the Guinness PRO12 whilst not necessarily playing their best rugby is an ability not to be sniffed at.
"The boys summed it up in the changing room. Our leaders spoke and said we've come away with a win which was the important thing but it was not as good a performance as we have come to expect," he told Cardiff Blues' official website.
"We were a little bit sloppy in patches but when we stuck to the game plan we scored three good tries. When we got carried away and lost the ball in the final third against a decent defence we ended up camped in our own 22.
"There are positives to take but we definitely need to look to improve the performance going into Leinster next week.
"We don't underestimate coming here. It's a bit different to playing the Italian sides at home, they maybe don't travel consistently but here they are a very different side and a tough side to beat.
"It's a long season, there are a lot of tough games and we will have blips along the way whether losses or a poor performance. Today was an average performance but a win and we have to take the positives from that.
"We're four out of four going into a home game and if you had offered me that at the start of the season I would have bitten your hand off."
Guinness PRO12 Blues News
63x46.png){kind=logo}