Andrew Trimble runs in for his try in Ulster's Magners League win
Ulster 14 (14)
Tries: Boss, Trimble
Cons: Humphreys 2
Dragons 7 (7)
Tries: A Brew
Ulster kept up the pressure on Magners League leaders Leinster but were made to fight every inch of the way by a dogged Newport Gwent Dragons side.
It seemed as though Ulster would run away with it after Isaac Boss and Andrew Trimble crossed for converted tries in quick succession.
But Dragons hit back before half-time through new Wales wing Aled Brew.
That proved enough for a losing bonus point as both sides defended their lines fiercely after the break.
Ulster started at a ferocious pace and had their visitors rocking in the opening exchanges at Ravenhill.
Stephen Ferris created a hole in the Dragons defence and Boss was on the number eight's shoulder to scoot away to the try line after just six minutes, David Humphreys converting.
On 50 minutes we'd silenced the crowd but we just didn't take our chances.
Dragons coach Paul Turner
A second try soon followed thanks to some great scavenging work from man-of-the-match Neil Best, robbing opposite blind-side Andrew Hall to release Trimble.
The winger added a cheeky dummy and step to raw pace that took him down the left touchline and then arcing under the posts for another seven pointer.
But Humphreys, playing his first match of the year, missed a penalty soon after the half-hour mark.
Gareth Wyatt, with a fine solo chip-and-chase, almost got the Dragons on the score-sheet but a stumble at the crucial moment allowed the defensive cover to get to the wing.
But it gave the Welsh heart and the Dragons pack produced a fine drive into the Ulster 22 that gave Brew space to power over after Phil Dolman's inside pass.
Ceri Sweeney's conversion meant that Ulster's lead had been cut to 14-7 at half-time.
Ulster started the second period as determinedly as they had the first and only good defensive work from Paul Emerick held up Tommy Bowe over the Dragons try line.
Bowe was again denied two minutes later as the wing spilled the ball going for the line under a clattering tackle from Brew.
Ulster returned the favour when it seemed Ben Daly must score, only for the Dragons hooker to be stopped in his tracks by Paul Steinmetz.
That sort of defence was needed again as the Dragons camped in the Ulster 22, but the home side held firm and eventually lifted the siege to secure the win.
Dragons coach Paul Turner:
"On 50 minutes we'd silenced the crowd but we just didn't take our chances.
"Ulster will probably feel themselves fortunate but we've come to the league champions and deserved a draw in the end.
"It's all part of our development and I'm really proud of the players, although perhaps we had too many unforced errors."
Ulster: B Cunningham; T Bowe, P Steinmetz, P Wallace, A Trimble; D Humphreys, I Boss; J Fitzpatrick, P Shields, S Best, J Harrison (capt), T Barker, N Best, K Dawson, S Ferris.
Replacements: S Philpott, B Young for S Best (54), R Caldwell, R Wilson for Dawson (59), K Campbell for Boss (77), K Maggs for Wallace (75), P McKenzie for Cunningham (55).
Dragons: Aled Thomas; Gareth Wyatt, Paul Emerick, Phil Dolman, Aled Brew; Ceri Sweeney, Gareth Cooper; Adam Black, Ben Daly, Jamie Corsi, Luke Charteris, Peter Sidoli, Andrew Hall, Jamie Ringer, Michael Owen (capt).
Replacements: Richard Wilkes, Gethin Robinson for Corsi (46-59; 73), Colin Charvis for Hall (41), Nic Fitisemanu for Owen (63), Richard Fussell, Mike Hercus, Alex Walker for Cooper (63).
Referee: David Changleng (Scotland).