Newport had earlier scored the first try of the game through back row Jevon Groves, converted by Lewis Robling who also kicked two decisive penalties in an error strewn match at Rodney Parade.
Cardiff were always within a shout of winning - Tom James scoring in the 18th minute and Dan Parks kicking two penalties while an effort from Ben Blair temporarily put them 14-13 ahead late on.
However Chavhanga had other ideas as Newport claimed a rare win over the Blues and also denied them moving into the top four of the RaboDirect PRO12.
Cardiff opened the scoring in the fourth minute after Groves was penalised following a high kick from Parks - the Blues fly-half slotting three points from just inside Newport's half.
However a matter of seconds later Groves made up for his mistake, pouncing on an incredibly loose pass from Mike Paterson to collect and score the first try of the night at Rodney Parade.
Robling kicked an easy conversion to make it 7-3 and then slotted an even easier penalty as the Dragons took the ascendancy in the opening 15 minutes.
However Robling's 100 per-cent record on the night didn't last much longer as just after the quarter of an hour mark the Newport fly-half sent a kick on halfway wide of the right post.
And the Dragons lead was soon cut down as Richie Rees ripped Anitelea Tuilagi of the ball and broke clear before feeding wing James for an easy score in the corner.
Parks couldn't convert and, despite the Dragons' scrum breaking down several times with 15 minutes left of the half, he pulled a penalty wide and a chance for Cardiff to take the lead was gone.
But Newport couldn't extend their lead either, Robling missing his second penalty on the trot after Cardiff scrum-half Rees was penalised for a high tackle on Aled Brew.
Robling made no mistake just after the break though while Parks was also successfully with a penalty himself 45 metres out as the score progressed to 13-11.
The penalty count was ticking over on a regular basis and after three straight from the Dragons, an offside from Brew the final nail in the coffin, Parks had another chance at goal but this time missed.
Cardiff gave away a cheap one themselves in the 58th minute but Steffan Jones, now on kicking duties, couldn't convert either - his effort hitting the lower part of the right post.
The Blues almost took the lead for the first time in the 62nd minute when Blair sent a perfectly weighted kick hurtling towards the Newport line before applying the pressure on Brew.
He was joined in doing so by Ceri Sweeney with Brew stumbling and James appearing to touch down however after consulting the Television Match Official it appeared Wayne Evans had beaten him to it.
Cardiff did take the lead six minutes later though - Blair kicking a penalty from the touchline after
Evans was adjudged to have deliberately stopped Rees attempting to get onto his own grubber kick.
But it lasted no more than four minutes as a moment of brilliance from Chavhanga effectively ended the game as a contest in Newport's favour.
|Newport Gwent Dragons Score Card|
|Cardiff Blues Score Card|