Welsh international duo Jenkins and Warburton are part of six changes for Cardiff Blues from side that played Ulster Rugby in the league last week.
Prop Scott Andrews, also part of the recent 6 Nations campaign for Wales, is the other change in the pack for the encounter that is being televised live on BT Sport.
Full Dan Fish returns to the starting line-up, following his recent exploits with Wales Sevens in Hong Kong, while Argentine ace Joaquin Tuculet is named in the centre.
The final change sees a call-up for in-form Richard Smith with the wing currently joint top try scorer in the European competition this season with five, alongside team-mate Lloyd Williams.
Lucas Amorosino and Tom Isaacs are ineligible for the Euro cup clash while Cory Allen (shoulder) and Rhys Patchell (concussion) also miss out through injury.
Dale McIntosh, Defence Coach at Cardiff Blues, said: “We’re looking forward to the game and it’s vital we have the right attitude. We won’t take them lightly and we understand the magnitude of the game.
“It’s the biggest game we’ve had for a few years and the atmosphere will be very special with it being a Welsh derby and the chance to make the semi-finals up for grabs.
“Dragons have some dangerous players in the back line and a well-coached pack and clinical set piece. We will have to be at our best to get the result we want.”
Cardiff Blues: 15 Dan Fish, 14 Alex Cuthbert, 13 Joaquin Tuculet, 12 Gavin Evans, 11 Richard Smith, 10 Gareth Anscombe, 9 Lloyd Williams; 1 Gethin Jenkins, 2 Matthew Rees (c), 3 Scott Andrews, 4 Jarrad Hoeata, 5 Lou Reed, 6 Josh Turnbull, 7 Sam Warburton, 8 Josh Navidi
Replacements: 16 Kristian Dacey, 17 Sam Hobbs, 18 Adam Jones, 19 Macauley Cook, 20 Ellis Jenkins, 21 Tavis Knoyle, 22 Simon Humberstone, 23 Gareth Davies