Smith returns at outside centre while Robinson is back on the wing as Blues look to return to winning ways in the league competition.
Hooker Marc Breeze starts the game, with Kristian Dacey ruled out through injury, while Macauley Cook moves to lock to partner Filo Paulo.
The final changes sees Rory Watts-Jones named at blindside flanker to join Josh Navidi and Robin Copeland in the back row.
Wales prop Gethin Jenkins returns among the replacements while hooker Rhys Williams will make his 50th appearance for the region if he comes off the bench.
Phil Davies said: "We played with real endeavour and physicality at Rodney Parade, but we were obviously disappointed by the result in Newport.
"However, the nature of Dominos Derby Series is that we face each other again almost immediately and have a chance to make amends.
"There will be a huge fired crowd at the Arms Park and I'm sure the atmosphere will be absolutely electric as we look to kick-off 2014 with an important result and move up the RaboDirect PRO12 table."
Tickets remain on sale NOW for the Dominos Derby Series clash with the Dragons at the Arms Park. Call the Ticket Office on 02920 302030 or click www.cardiffblues.com to buy online.
Cardiff Blues: 15 Leigh Halfpenny, 14 Alex Cuthbert, 13 Richard Smith, 12 Dafydd Hewitt, 11 Harry Robinson, 10 Rhys Patchell, 9 Lloyd Williams; 1 Sam Hobbs (c), 2 Marc Breeze, 3 Benoit Bourrust, 4 Macauley Cook, 5 Filo Paulo, 6 Rory Watts-Jones, 7 Josh Navidi, 8 Robin Copeland.
Replacements: 16 Rhys Williams, 17 Gethin Jenkins, 18 Scott Andrews, 19 Chris Dicomidis, 20 Ellis Jenkins, 21 Lewis Jones, 22 Gareth Davies, 23 Gavin Evans
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