Most importantly, the result ensured Ulster's presence in the end of season play-offs. Heineken Cup finalists Leinster will welcome them to the RDS next Friday night.
The Dragons had won three of their previous four games under newly-appointed head coach Darren Edwards, and Tom Riley's 57th-minute try saw them pressurise Ulster at 20-13 down.
Nonetheless, Ulster deservedly saw out a win which keeps alive their hopes of lifting silverware in Brian McLaughlin's second year in charge.
It was a stellar first half performance that won it for the men in white, with some opportunistic attacking from Adam D'Arcy and Craig Gilroy almost resulting in an early try.
The deadlock was broken by a sixth minute penalty from Ian Humphreys and quickly followed by a first try from Spence, the recently-named Irish Players' Young Player of the Year.
The 21-year-old centre picked up possession near halfway and exposed some poor defending from the Dragons on a devastating diagonal run right through to the try-line, evading a last-ditch challenge from Steffan Jones.
A penalty from Matthew Jones, who came on as a blood replacement, got the Dragons on the mark, but Spence and Ulster were celebrating again just four minutes later.
A powerful run from number 8 Robbie Diack saw Ulster gain good yardage. The visitors maintain possession and Australian full-back D'Arcy managed to flick the ball back inside, just before being bundled into touch, for Spence to stretch over for a five-pointer.
Chris Henry spoke about the importance of a strong start against the Dragons, having reviewed the sides' recent meetings, and so it proved for Ulster who were good value for their 13-3 lead.
Tovey returned for Jones and was successful with a 34th minute penalty before Ulster scored their third try of the night.
The provincial side signalled their intent by kicking a penalty to touch and although the lineout did not go to plan, influential flanker Wannenburg collected the ball ten metres out and brushed Tovey aside to dot down and allow Humphreys an easier conversion.
Given their recent form, it was inevitable that the Dragons would come back into contention. Jones, who was reintroduced for Tovey, watched his penalty attempt bounce back off the right hand post.
Rain showers during the break meant the playing conditions worsened but the men of Gwent managed to reduce the arrears from 20-6 to 20-13 when some patient build-up play was rewarded by a converted try.
After five minutes of intense pressure, the Ulster defence eventually gave way when scrum half Wayne Evans and Jones teed up centre Riley for his fourth try of the league campaign. Jones flung over the conversion to inspire further hopes of a comeback win for the hosts.
But defences were on top for the remainder, the only other scoring chance being a missed penalty from Humphreys after 63 minutes.
With Leinster cutting loose against Glasgow Warriors, Ulster's chances of finishing second in the table faded. The Dragons, who also lost in Belfast earlier in the season, were already resigned to finishing seventh overall, behind their Welsh rivals Cardiff (sixth), the Scarlets (fifth) and the Ospreys (fourth).
|Newport Gwent Dragons Score Card|
|Ulster Rugby Score Card|