Having lost Wales' Luke Charteris and Aled Brew in the summer, the emphatic win made for the perfect start to the Dragons' season - and Jones will hope to have strengthened his own international credentials.
His opposite number, former Italy fly-half Luciano Orquera, scored Zebre's only points in a disappointing start for a squad boasting over 400 caps for the Azzurri - however their Italian counterparts, Benetton Treviso fared significantly better against the champion Ospreys.
Kris Burton kicked Treviso to a shock 12-6 win in torrid conditions at the Stadio di Monigo after Wales lock Ian Evans picked up a costly first-half red card.
The Italy full-back handled the wind better than his goal-kicking counterpart, Dan Biggar, who missed three attempts at goal.
The Ospreys will look to make amends next week as they take on the night's other winner, an improving Ulster team who overcame Glasgow 18-10 at Ravenhill.
In the absence of internationals Tommy Bowe and Stephen Ferris, given extra time to recover from their summer tour, two of Ulster's rising stars, wingers Mike Allen and Craig Gilroy crossed to give their side the opening-day win.
The second-half introduction of Scotland internationals Ruaridh Jackson and Chris Cusiter brought last year's semi-finalists to within a score with ten minutes to play, but the boot of Niall O'Connor - on for an injured Paddy Jackson - secured Ulster's win with a late penalty.