Danny Wilson’s men looked set for defeat trailing 17-6 in the final quarter of a tense clash before the late twist.
A penalty try – after a powerful rolling maul – and score from wing ace Tom James put Cardiff Blues back within two points.
And then, in the final minute, Patchell stroked over a penalty under huge pressure to secure the points in memorable scenes.
It was a true derby encounter with a red-hot atmosphere at kick-off with both teams trading kicks in the early stages as they hunted a platform to play from.
Visiting wing James broke away from tackles after fielding one of those high balls, but it was the home side who opened the scoring courtesy of a drop goal from fly half Jones on seven minutes.
Opposite number Jarrod Evans rose highest to claim a huge up and under before young centre Garyn Smith charged down a kick in a highly charged opening period.
However, more home territory, after accidental offside against Cardiff Blues, saw the Dragons strike and score the opening try of the match as the ball was flung down the line at pace to left wing Hewitt who touched down under pressure in the corner.
Cardiff Blues looked for a quick response to steady the ship and Alex Cuthbert did break the Dragons line, after a neat inside ball from Evans, and his pass almost fed the supporting Smith to break away and clear.
But a penalty in the build-up went to the visitors and Patchell slotted the resulting kick.
Wilson’s men put together some sustained phase play, as the forwards took the ball on to gain yards, but a penalty for holding on saw momentum lost as the game moved towards the mid-point of a pulsating opening half.
Turnover ball sprung Samoa centre Rey Lee-Lo into space and when the penalty was won at the breakdown the resulting kick from Patchell ate into the lead some more.
It was fast and furious at times in midfield as both teams looked to take advantage of spilled ball in contact and knock-ons from repeatedly contested high balls.
A booming long kick into space from Patchell forced the home side onto the back foot, but Dragons were enjoying some success on their own kicking game as they traded possession and slowly forced their way back into the Blues half.
The visitors were enjoying dominance in the scrum, but often getting little reward from the officials, as a tense and tight derby entered the final five minutes of the first period.
However, one final slice of action saw a penalty awarded to the Dragons, for side entry against then Blues cover defence, allowing home playmaker Jones to extend the lead to 11-6 at the break.
The dose was repeated three minutes after the break, for a similar offence, with Jones once more showing his accuracy with the boot.
Macauley Cook replaced Lou Reed while a sustained period of kicking this time went in the favour of Cardiff Blues as Patchell found a huge touch finder.
Offside against Rynard Landman gave the visitors an attacking lineout, as Patchell kicked deep, but the home side were unloaded some big tackles in the collisions and eventually the ball was lost.
A tactical change saw Patchell move to fly half and Dan Fish come on at full back as Cardiff Blues looked for fresh direction.
However, it was the hosts who clicked with a brilliant breakout from deep seeing try scorer Hewitt break two tackles and crank the volume up another level inside Rodney Parade.
Cardiff Blues, though, turned over ball and then won a scrum penalty as they showed huge resolve under huge pressure.
Cory Allen entered the fray on his comeback, to play his first rugby since the World Cup, after 52 minutes as Wilson started to unload his bench searching for extras firepower and a spark.
A charged down drop goal from Jones went from bad to worse for Blues as a deflected touch on the way through from Navidi meant the clearing kick out from Fish went right back and gave Dragons an attacking lineout five metres from the line.
The forwards needed no second invite and charged for the line before a penalty gave Jones a simple kick for a 17-6 lead to the delight of the home support with 20 minutes left.
Cardiff Blues needed a score quick and had the opportunity as Patchell went to the corner after Dragons sealed off. They duly drove the driving maul forward and as Dragons cynically tried to stop it a penalty try was rightly awarded and Lewis Evans yellow carded.
The home side immediately looked to play for territory being a man down, but they were helped when a penalty for side entry at the breakdown gave Jason Tovey a simple kick for a seven-point lead.
However, Blues countered and some slick hands and a mazy break from Fish split the home side wide open and the supporting runner James slid over. Patchell, though, missed the conversion from out wide as Dragons kept a two-point lead.
More drama saw Lee-Lo break down the middle and when the ball was spun wide a run from James caused panic and won the penalty.
Up stepped Patchell to silence the boo boys and moments later Lloyd Williams kicked the ball out to start the celebrations.
Timeline:
07m Jones dg 3-0
11m Hewitt t 8-0
14m Patchell p 8-3
23m Patchell p 8-6
39m Jones p 11-6
43m Jones p 14-6
61m Jones p 17-6
66m Penalty t Patchell c 17-13
72m Tovey p 20-13
74m James t 20-18
79m Patchell p 20-21
Cardiff Blues: 15 Rhys Patchell, 14 Alex Cuthbert, 13 Garyn Smith (Allen 52), 12 Rey Lee-Lo, 11 Tom James, 10 Jarrod Evans (Fish 50), 9 Lloyd Williams; 1 Gethin Jenkins (Hobbs 56), 2 Kristian Dacey (E Lewis 63), 3 Taufa’ao Filise (D Lewis 56), 4 Lou Reed (Cook 46), 5 James Down, 6 Josh Turnbull, 7 Josh Navidi, 8 Manoa Vosawai (Dolan 66)
Replacements: 16 Ethan Lewis, 17 Sam Hobbs, 18 Dillon Lewis, 19 Macauley Cook, 20 Cam Dolan, 21 Tavis Knoyle, 22 Cory Allen, 23 Dan Fish