Fly-half Ceri Sweeney also returned from World Cup duty with Wales to kick 16 points and help the region get back on track after three successive league losses.
Missing 13 players due to injury or rest from Ireland's World Cup campaign, Ulster travelled looking to rediscover their form after a flat display in last week's 24-10 defeat in Edinburgh.
But the visitors got off to a decidedly poor start by conceding eight points in as many minutes - Sweeney kicked a sixth-minute penalty and moments later, another returning Welsh international Kevin Morgan teed up winger Wyatt for an unconverted try in the right corner.
Ulster awoke from their slumber with a couple of punchy drives from their forwards, however turnovers were robbing their of inviting field position. Still, young fly-half Niall O'Connor did open the Irish side's account in the 17th-minute with a penalty from distance.
Some rock solid defending from Ulster kept the home side from adding to their tally, but losing flanker Matt McCullough to a needless 34th-minute yellow card - he was punished for repeated ruck infringements - had Mark McCall's men under extra pressure.
The on-form Sweeney kicked the subsequent penalty through the posts from 40-plus metres and he repeated the trick from closer range in injury-time, following hands in the ruck from Ulster, for a 14-3 interval lead for the Dragons.
Having beaten the Dragons four times since a 13-11 defeat at this venue in February 2005, Ulster came out for the second half with renewed fight. Their early efforts were rewarded with a second successful penalty from O'Connor, punishing an offside from the hosts.
The Dragons took their time to get going after the resumption but a second yellow card for an Ulster player - flanker David Pollock was sin-binned for diving over the top of a ruck when the Dragons were within try-scoring range - flicked the switch for Paul Turner's men to set out the win.
Sweeney kicked the resulting penalty from close to the posts and on 58 minutes, after good hands from Wayne Evans and Steve Jones, centre Gomer Davies took a pass from Wayne Evans to hare in under the posts for a converted try which had the Dragons 24-6 to the good.
Ulster, who threw on Italian World Cup lock Carlo Del Fava for his league debut, hit back immediately and sent prop Tom Court over for a 60th-minute try, after scrum half Paul Marshall had been stopped just short of the whitewash.
O'Connor missed the conversion and as the minutes ticked by, Ulster's chances of launching a comeback or at least notching a losing bonus point faded.
The Dragons were content to play keep ball and they rounded off a morale-boosting win - their first since their opening weekend success at the Scarlets - with an injury-time seven-pointer from lock Charteris.
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| Newport Gwent Dragons Score Card | |||||
| Name | Tries | Conv | Pen | Drop | Pts |
|---|---|---|---|---|---|
| Gareth Wyatt | 1 | 5 | |||
| Ceri Sweeney | 2 | 4 | 16 | ||
| Luke Charteris | 1 | 5 | |||
| Rhodri Gomer Davies | 1 | 5 | |||
| Total | 3 | 2 | 4 | 31 | |
| Ulster Rugby Score Card | |||||
| Name | Tries | Conv | Pen | Drop | Pts |
|---|---|---|---|---|---|
| Tom Court | 1 | 5 | |||
| Niall O'Connor | 2 | 6 | |||
| Total | 1 | 2 | 11 | ||
| ||||||||||||||||||||||||||
