That left Lyn Jones' side seeking a first competition double over their near neighbours for 10 years, but it was not to be.
Patchell kicked the hosts into an early lead and two more shots, from Halfpenny, gave them a 9-0 advantage a packed Arms Park.
The Dragons had spent most of the opening exchanges in their own territory, but they comfortably dealt with the attacking threats posed by the Blues.
Fly-half Patchell's mid-range kicks to the flanks had paid no dividends for his side either.
And his final effort before departing injured gave outstanding visiting full-back Dan Evans the chance to launch a productive counter-attack.
Centre Ashley Smith gathered Patchell's speculative kick and his pass sent Evans away and after drawing Halfpenny's attention in defence, the Dragons full-back gave wing Harries a 20-metre run to the line.
Patchell then departed and boss Davies later said he had suffered a shoulder injury' although television footage seemed to show the Wales fly-half had sustained a knee blow.
Dragons stand-off Tovey, who missed two first-half penalties, added the conversion to Harries' try and the penalty that gave Lyn Jones' side a 10-9 half-time lead.
However, anyone hoping the Dragons try would spark more memorable attacking moments to savour was to be disappointed.
Harries' try proved the game's highlight as the visiting defence continued to thwart the Blues' attacks.
The frustration in the Blues' ranks manifested itself when Wales wing Alex Cuthbert was penalised for a post-breakdown shove.
But with their forwards dominating the visitors, Halfpenny was given the chance to make amends for his two missed penalty shots.
The 2013 British and Irish Lions star kicked three second-half shots, two of them to put his side ahead.
Patchell's replacement Gareth Davies dropped a goal as the home side edged towards victory.
And Halfpenny sealed victory with the game's final kick.
Leigh Halfpenny; Alex Cuthbert, Richard Smith, Dafydd Hewitt, Harry Robinson; Rhys Patchell, Lloyd Williams; 1 Sam Hobbs (capt), Marc Breeze, Benoit Bourrust, Macauley Cook, Filo Paulo, Rory Watts-Jones, Robin Copeland, Josh Navidi.
Replacements: Rhys Williams, Gethin Jenkins, Scott Andrews, Chris Dicomidis, Ellis Jenkins, Lewis Jones, Gareth Davies, Gavin Evans.
Daniel Evans; Will Harries, Pat Leach, Ashley Smith, Matthew Pewtner; Jason Tovey, Wayne Evans; Owen Evans, T Rhys Thomas, Dan Way, Matthew Screech, Rob Sidoli (capt), Netani Talei, Toby Faletau, Lewis Evans.
Replacements: Sam Parry, Aaron Coundley, Francisco Chaparro, Adam Jones, Nic Cudd, Richie Rees, Steffan Jones, Ross Wardle.
Leighton Hodges (WRU)
Neil Hennessy, Gwyn Morris (both WRU)
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.