It was just a second win in seven matches for the Dragons, who were humbled 60-3 last time out by Glasgow Warriors, and it was a first away win in the RaboDirect PRO12 since March 2012.
For Zebre it was another case of close but no cigar, having also come agonisingly near to defeating four of the RaboDirect PRO12 sides.
A cagey opening 20 minutes saw Jones miss his first effort from the tee on six minutes before Zebre scrum-half Alberto Chillon followed suit for the home side on 18 minutes.
Chillon did draw first blood however for Zebre, booting his side into a 3-0 lead on 21 minutes but just after the half hour mark, he was punished for another wayward kick.
Just a minute later, Dragons fly-half Jones levelled things up but in a topsy turvy first half, Dragons prop Nathan Buck was then sent to the sin bin.
And Zebre took full advantage with centre Matteo Pratichetti forcing his way over for the first try of the match with just a minute left of the first half.
Chillon converted to give Zebre a healthy seven-point lead at half-time and the hosts moved even further in front early in the second half.
No sooner had Buck returned from the sin bin that Phil Price, the Dragons' other prop, followed him for a ten minute spell on the sidelines and Chillon was on target with another penalty for the home side.
Zebre were unable to capitalise further on their numerical advantage however and when Price returned, it was the home side's turn to play ten minutes with 14 men after full-back Alberto Benettin was shown a yellow card.
From the resulting penalty, Jones kicked his side back to within seven points and the margin was just two on 61 minutes when Dragons second row Jevon Groves dotted down.
With the wind in their sails, the Dragons smelt a victory and Jones made no mistake from the tee on 66 minutes to hand his side the lead for the first time in the match.
Zebre rallied, desperate to secure victory over the side just one place above them in the table, but try as they might, they could not find a way through and the Dragons clung on for a hard-earned win.
|Zebre Score Card|
|Newport Gwent Dragons Score Card|