It was a rousing first-half performance by the Welshmen, who are more used to fighting at the other end of the league rather than the top end.
Dan Evans grabbed two first-half tries with others coming from centre Andy Tuilagi and wing Will Harries while wing Tom Prydie kicked four conversions and two penalties and fly-half Steffan Jones added a drop-goal against two penalties for Zebre's fly-half Luciano Orquera.
The Dragons had their four tries and bonus point in the bag by the break with probable and possible Welsh caps for the big Autumn Test matches against Argentina, Samoa, New Zealand and Australia watched by national coach Warren Gatland and assistant Neil Jenkins from the stand.
Gatland would have been impressed by the very early season form of regular Wales stars Dan Lydiate and Toby Faetau, who both had good run-outs against a Zebre side who showed plenty of fighting spirit for their debut in the competition.
However, as reasonable as the Italians were in attack, their defence was found wanting when stretched, leaving them way off the pace at 34-6 at half-time.
Full-back Evans had a glorious 40 minutes. The Wales Under-20 cap, making his debut for the Gwent side after five seasons at the Scarlets, set-up the first try of the campaign for powerful Tuilagi on 13 minutes before scoring two himself towards the end of the half.
But none of those three tries matched the cracker on 19 minutes which came after a thumping tackle inside the home 22 saw hooker Steve Jones, another on Gatland's possible list, retrieve the ball.
The Dragons skipper ran out and gave it to Prydie before the ex-Wales wing produced a piece of quick-thinking.
He was tackled into touch but threw the ball straight back into play, found Jones who laid the ball to Harries to storm over.
Jones booted a drop-goal while Prydie added all four conversions to an early penalty against two penalties from Zebre stand-off Lucian Orquera.
The concern for Dragons coach Darren Edwards, though, must have been how his side dropped the intensity in the second half having established such a big lead.
Zebre, with the pack working as a unit and a wily scrum-half in 14-times Italy capped Tito Tebaldi behind, put pressure on the Welshmen for quite a while in the second period but failed to find a route to the line.
As the clocked ticked over the hour mark, the Dragons finally got the scoreboard moving again when Zebre infringed in front of their posts and Prydie popped over his second penalty.
To their credit, the Italians were enterprising in attack all night with the ball in hand and were not worried about throwing it around via the forwards or backs - which kept the home side on their toes.
But it was not a good second-half for the Dragons.
Nevertheless, Gatland and Jenkins left the ground a few minutes before the end having seen a job well done - although it goes from one extreme to the next in the Dragons' second league game where they play last season's runners-up and Heineken Cup champions Leinster in Dublin.
New Ulster coach Mark Anscombe had the perfect start to his tenure as tries from wingers Michael Allen and Craig Gilroy brought Ulster a win over Glasgow.
Anscombe's youthful selection - the coach was missing a raft of frontline players - showed great maturity to see off a much more experienced Scottish side who also had new coach Gregor Townsend at the helm for his first competitive start.
Ulster were always the hungrier side and big performances from Nick Williams and John Afoa along with youngsters Allen and Luke Marshall helped bag them the four points, though their winning margin would have been greater had Niall O'Connor been more accurate from the tee.
After an opening 10 minutes in which neither side made much impression, Ulster opened their account with an O'Connor penalty with the former Connacht player's first touch after he replaced the injured Paddy Jackson.
The Warriors, though, evened matters up 10 minutes later with a Duncan Weir penalty after Nick Williams was penalised at the breakdown.
Ulster then came close when Williams lost the ball over the line before O'Connor hit an upright with a 27th-minute penalty.
The fly-half then missed again with a similar chance on the half-hour but Ulster again responded through their pack and one driving maul for the Warriors' line resulted in Glasgow winger - and former Ulster player - Tommy Seymour being sin-binned for dragging the maul down.
The net result was a series of scrums near Glasgow's line and ultimately Williams drove off the base, linked with Stevenson and Jared Payne's loopy skip pass put Allen in at Seymour's corner for a score which O'Connor could not convert.
The half ended with Weir attempting a drop goal which sailed left of the posts and Ulster went in leading 8-3.
They started the second half in perfect fashion when Craig Gilroy intercepted Weir's pass and ran all the way in under the posts from just outside his own 22, with O'Connor this time making no mistake with the extras to put Ulster 15-3 to the good.
The game then became disjointed as the benches were emptied and then just after the hour, Glasgow replacement Ruaridh Jackson's 63rd-minute penalty hit an upright and Tom Court - who had just arrived to make his 100th Ulster appearance - dived on the ball as Ulster cleared the danger.
But then, on a rare attack, Jackson worked Seymour clear and the winger rounded two defenders to score before Jackson then added the conversion to narrow Ulster's lead to 15-10.
Ulster were then unable to build on their lead when O'Connor was again wide with a 72nd-minute penalty attempt but did hit one in the last minute.
And also in Rabodirect Pro12 action, the boot ruled the proceedings as Ospreys slipped to a 12-6 defeat in their opening match of the season in Treviso.
Six penalties were the extent of the scoring in Treviso, with Dan Biggar kicking both for the visitors.
However, they paid for having to play three quarters of the game with 14 men, following the dismissal of Ian Evans for two yellow cards.
Playing into a strong wind before the break and a man light, the Ospreys trailed by nine points at the turnaround.
They dominated the final 40 minutes but had to settle for a losing bonus point as they launched the defence of their Pro12 crown.
A penalty for coming in from the side provided Treviso with an early opportunity to take the lead and despite his unconvincing kick that just about cleared the crossbar, Kristopher Burton was able to grab the first points of the night, the Italians going 3-0 up in the sixth minute.
The Ospreys were reduced to 14 just a couple of minutes later, Evans sent to the sin-bin for killing the ball on the floor after finding himself isolated.
Burton then punished the visitors for two offside decisions, leaving them 9-0 down after 14 minutes.
Bigger kicked the Ospreys' first points after a rare attack resulted in a penalty but the Welsh province struggled in the conditions as Treviso dominated the territory.
However, the Italians' progress was halted abruptly by a high tackle from Evans, back on the field just a matter of minutes, leaving the big second row on the receiving end of a second yellow card - and the Ospreys to play 50 minutes at a numerical disadvantage.
Burton then compounded the Ospreys' woes, slotting his fourth penalty of the night before the break.
The visitors started the second half confidently and Biggar soon reduced the margin to six points when Treviso tighthead Ignacio Fernandez-Rouyet was penalised for not rolling away and shown a yellow card.
Ospreys centre Ashley Beck almost crossed the line but was adjudged to have been held up by Tommaso Iannone before Treviso were down to 14 again when replacement lock Dean Budd was yellow carded for a dangerous tackle on Richard Fussell.
Biggar then missed another kick on goal, his third of the night, as the reigning champions failed to find a cutting edge against dogged Italian defence.