Second half tries from Ceri Sweeney and Gavin Evans, allied to a 10-point kicking haul from Ben Blair, helped the Cardiff men claim their seventh successive away win in all competitions.
The Dragons, who had only been beaten once at home since March of last year, had built an 8-0 lead by the end of the first half.
Ben Castle broke through for a try, adding to an earlier penalty from James Arlidge, but two penalties either side of half-time from Blair closed the gap in an edge of the seat tussle.
The crucial scores for Cardiff came after 60 and 62 minutes when Sweeney and Evans made the line in quick succession, with Blair converting both efforts.
Dragons captain Tom Willis and Cardiff prop Rhys Thomas were sin-binned for scuffling and the hosts fought their way to a late losing bonus point as Arlidge knocked over his third penalty with the last kick of the game.
The result leaves Cardiff in fifth place and still in contention to reach the final four, with defending champions and play-off rivals Munster visiting the Cardiff City Stadium in two weeks' time.
The Dragons have not beaten the Blues since March 2006 - that is a run of seven straight defeats - and it will take a mathematical miracle for Paul Turner's men, who are down in seventh position, to squeeze into the play-offs.
Both sides were hit by injuries and the unavailability of players ahead of the match. Significantly, the Blues lost Wales prop Gethin Jenkins with a foot injury plus flanker Martyn Williams and in-form New Zealand centre Casey Laulala.
The Dragons lost five players from the squad that beat Edinburgh last Sunday, including talismanic out-half Jason Tovey, who has concussion, and Wales' giant lock Luke Charteris.
And with play-off places and local bragging rights on the line for the teams, neither side wanted to give an inch in the opening moments.
But, after Wales winger Leigh Halfpenny missed a long range penalty in the third minute, the Dragons went ahead when out-half Arlidge booted a penalty.
They then went 8-0 up when a move started by a drive from skipper Willis ended with flanker Gavin Thomas feeding prop Castle for an unconverted touchdown in the corner.
The intensity continued at a high level throughout an absorbing first half, with the Dragons' industry and skill keeping them ahead.
Cardiff centre Jamie Roberts carried forward with intent and the Dragons infringed on their 22 for full-back Blair to comfortably boot his opening penalty.
However, the Blues then lost the services of big number 8 Andy Powell was led off the pitch with a calf injury, which could rule him out for next Saturday's Amlin Challenge Cup semi-final against London Wasps.
The Dragons nearly got a second try when a surge into the Cardiff 22 saw number 8 Toby Faletau pick up from a ruck and feed winger Will Harries to go over in the corner but referee Alain Rolland ruled it out for a forward pass.
Head coach Dai Young must have given the Blues a stern word at half-time because they came out with much more purpose after the break and forced the hosts into mistakes.
Blair had two kickable penalties but pushed both wide of the posts before taking his third opportunity from 20 metres when the Dragons strayed offside.
As Young's charges continued to up the ante, they picked up two all-important tries in the space of three minutes on the hour mark that put distance between them and the Dragons.
It was Sweeney, the former Dragons fly-half, who bagged the first of those two when he booted a high kick into the home 22 only for full-back Martyn Thomas to slip and allow Sweeney to gather the ball, beat two defenders and score.
Then an excellent move down the right saw Halfpenny scorch up the touchlin and set up replacement replacement Gavin Evans for a run-in. Blair converted both to give his side a 20-8 lead going into the final quarter.
Willis and Rhys Thomas then saw yellow for getting involved in a bust-up and while they were off, Dragons full-back Martyn Thomas sustained a horrible ankle injury.
He was stretchered off and taken straight to hospital for surgery, with Roberts (knee), Dragons centre Ashley Smith (knee) and Blues scrum half Richie Rees (ankle) also suffering injuries during an attritional second period.
The Dragons tried to hit back with a try of their own but excellent defending from man-of-the-match Ma'ama Molitika and replacement scrum half Lloyd Williams saw the Blues keep their line intact.
Rhodri Gomer-Davies looked like he had been held back by try scorer Evans as an Arlidge-led attack carved open the visitors' defence, but play carried on and Evans eventually cleared the danger.
In the end, the Dragons had to settle for a losing bonus as two penalties from Arlidge, after 68 and 80 minutes, closed the margin to six points.
Speaking after the game, Dragons coach Paul Turner said: "I'm a little bit despondent. A couple of decisions went well against us - in the first half with advantage over - really killed us and the bust up the middle in the second half which was a yellow card and a possible try under the sticks and everybody in the ground saw it and the officials and two touch judges just missed it.
"So they were crucial moments and one of Ceri (Sweeney's) famous slices has gone and killed us.
"But in fairness we didn't clear our lines well enough in that crucial period in the first 20 minutes of the second half.
"We had ample opportunities to do that and we've come up short on that. The game went from us in a crucial five-minute period."
Pleased with his side's second half display, Blues boss Dai Young said: "We failed to get much go-forward ball (in the first half), so we talked about putting extra numbers in there, which would give us a bit of go-forward and obviously then if we can get some go-forward we can get behind them, which proved to be the case.
"I was really pleased with the way the boys really fronted up in the second half because it was a really tough encounter.
"The most important thing is coming here and winning. There's been a lot of talk about the Dragons this season and they've had an excellent season - you can't take that away from them.
"But we're a proud bunch and wanted to come here and win first and foremost. If we're lucky enough to get into the play-offs, great, but it's a long shot because it's pretty much out of our hands."
|Newport Gwent Dragons Score Card|
|Cardiff Blues Score Card|