Blues dug deep and hit back with in-form hooker Kristian Dacey scoring in a second successive Welsh derby before a penalty from Leigh Halfpenny drew the score level at the interval after a bruising opening half.
Halfpenny did nudge Blues ahead at the start of the second period, but a yellow card to Robin Copeland was followed by a series of penalties from Tovey as the home side slowly took control.
A thrilling final ten minutes saw both teams give everything, but it was the hosts who took the honours as Blues were left to contend a second narrow Welsh derby loss over the festive season.
Director of Rugby Phil Davies and his team must now regroup before the teams meet again on New Year's Day at the Arms Park for the second installment in what is sure to be a brutal encounter.
The game started to the backdrop of a deafening home roar and captain Andrew Coombs carried into contact at pace as Dragons started the clash with real tempo and intent. Several powerful runs were withheld by Blues, but a penalty for offside was awarded and up stepped Tovey to open the scoring.
Alex Cuthbert almost found a yard of space down the right wing, as he combined with Halfpenny, while Dragons continued to run hard and straight to test the Blues defence. Will Harries broke a tackle to secure a penalty and a kick to the corner, but the alert Dan Fish stopped the ball going dead and returned it to minimise the damage.
The fit-again Rhys Patchell looked to set Blues away from deep, after Macauley Cook pounced on a loose ball at the breakdown, but after finding Gavin Evans with an overhead pass the move broke down.
Dragons went wide left at pace and Harries got around the back and in on Halfpenny forcing the full back to make a fine tackle to stop him in full flow as the home side threatened an opening try.
Blues looked to unlock Dragons with Patchell showing invention as he chipped in behind but as he went to collect the ball he clattered Dan Evans in the air and the penalty went against the visiting fly half.
A superb training ground move saw Dragons score the opening try as a short line out was cleverly popped into the path of Faletau and he tore through a huge gap and raced to the line unopposed. Tovey added the extras for a 10-0 lead after 17 minutes in Newport.
The visitors looked to respond with Sam Hobbs and Josh Navidi hurtling into contact with the ball, after Evans flicked the restart back. But as they looked for width the ball was spilled forward and momentum lost.
More scintillating back play and quick handling in the tackle from Hallam Amos opened up Blues once more and Fish was forced to mop up the danger and hurriedly kick into touch.
Blues got back into the game on 25 minutes when initial strong work, from Halfpenny from deep and Cook on the wing, was rewarded as Dacey punched through a home tackle and kept his feet to slide over. Halfpenny added the extras to reduce the lead to 10-7.
Patchell was next to spot half a yard and exploit it before feeding Halfpenny on his shoulder. But with quick ball needed the possession was lost as a low pass failed to find Fish on his wing and minutes later a forward pass stopped the flier as he looked to take off.
On the opposite flank a neat move from Ashley Smith and Patrick Leach freed up space for Amos, but his pass went forward as he looked to offload as he was bundled into the sidelines.
The game was becoming a huge physical test for both sides as huge tackle after huge tackle flew in. Cuthbert looked to add some finesse to the occasion with a chip in behind to chase that the alert Amos picked off.
A big scrum from Blues on the stroke of half-time secured a penalty from the whistle of Ian Davies. It gave Halfpenny the chance to level the scores and he made no mistake with a low drilled effort.
Netani Talei broke down the middle in the opening moments of the second half to send pulses racing, however great work from Hobbs on the floor turned over ball.
The Dragons thought they were over when slick handling sent Smith over for a score as Rodney Parade erupted. But after consulting with the TMO the try was chalked off for obstruction in the build-up.
The home crowd was even more incensed two minutes later when a penalty at the breakdown allowed Halfpenny to kick Blues ahead for a first time in the game.
Try scorer Dacey hobbled off to be replaced by Rhys Williams ten minutes into the second half while a lineout infringement gave Tovey a kick to level the game once more.
Seconds later a clean line break at the restart, from the rampaging Smith, again put Dragons on the front foot and another penalty from Tovey nudged the hosts ahead.
Things went from bad to worse for Blues as Robin Copeland was yellow carded for pulling down a driving lineout and Dragons immediately stepped up the intensity to try and land a crushing blow.
Tovey added his fourth penalty of the afternoon as Dragons opened up a six-point advantage with a quarter of the game left.
The penalty count was now piling up against the visitors and Tovey was not in an unforgiving mood as he slotted another kick on 66 minutes.
Cuthbert nearly sparked a break from deep, as he picked up a stray pass and looked to burst Halfpenny ended the run of Tovey kicks to cut the lead to 22-16 with ten minutes remaining of an absorbing encounter.
A hack ahead from Cook, after Evans failed to pick up a spitting low grubber from Halfpenny, gave Blues late territory. But after the forwards looked to power up close the ball was lost forward.
One final attack saw Dragons force a five-metre scrum, after the ball was hacked forward in midfield. But Blues held firm and Tovey missed a drop goal on the whistle as the visitors claimed the consolation of a losing bonus point in Newport.
03m Tovey p 3-0
16m Faletau t Tovey c 10-0
25m Dacey t Halfpenny c 10-7
40m Halfpenny 10-10
46m Halfpenny p 10-13
51m Tovey p 13-13
53m Tovey p 16-13
62m Tovey p 19-13
66m Tovey p 22-13
69m Halfpenny p 22-16
Cardiff Blues: 15 Leigh Halfpenny, 14 Alex Cuthbert, 13 Gavin Evans, 12 Dafydd Hewitt, 11 Dan Fish, 10 Rhys Patchell (Davies 69), 9 Lloyd Williams; 1 Sam Hobbs, 2 Kristian Dacey (Williams 50), 3 Benoit Bourrust (Andrews 59), 4 Chris Dicomidis, 5 Filo Paulo, 6 Macauley Cook, 7 Josh Navidi, 8 Robin Copeland.
Replacements: 16 Rhys Williams, 17 Thomas Davies, 18 Scott Andrews, 19 Ellis Jenkins, 20 Rory Watts-Jones, 21 Lewis Jones, 22 Gareth Davies, 23 Richard Smith