A lightening quick start from the home side saw Rhys Patchell and Lloyd Williams score in the opening 12 minutes as Blues looked to take complete control from the start.
Grenoble showed plenty of fighting spirit in the opening half and two kicks from James Hart kept them in touch at 15-6 at half-time.
Wales star Sam Warburton repeated the home fast start in the second half with a try before wing Richard Smith grabbed the try bonus point on the hour after a sweeping team move.
More superb handling saw Josh Turnbull over for a fifth try to complete an impressive opening day in the tournament for Blues.
Top14 side Grenoble showed plenty of invention in the opening minutes and went straight on the attack with Geoffroy Messina breaking the line before slick handling freed hooker Anthony Hegarty.
The all-action Manoa Vosawai rumbled into contact before a big clearing kick from Gareth Davies relieved early visiting pressure.
Filo Paulo and Jarred Hoeata unloaded huge tackles as the French side was driven back on halfway. Gavin Evans then pounced at the breakdown to win a penalty as Blues defence held firm in the opening six minutes.
The first attack saw the forwards and backs combine brilliantly for several minutes with Williams freeing up Filo Paulo and Macauley Cook before Patchell almost freed Evans with a pop pass out of the tackle.
Blues were linking the play superbly well and the pressure finally told as Davies looped around, after battering runs from Vosawai and Matthew Rees, and fired a flat pass to Patchell who stepped inside and raced for the line.
Richard Smith went straight on the attack from the restart as he found space down the right wing. A penalty for offside on halfway saw Patchell fire a kick into the corner as Blues looked to turn the screw early on.
The forwards went to work and drive up close before Rees and Sam Hobbs crashed towards the whitewash.
The ball was stopped short, but alert scrum half Williams quickly dotted down amongst the bodies for a 12-0 lead after as many minutes, with Patchell’s conversion off the post.
Paulo crunched French scrum half James Hart to force a turnover and Blues looked to attack from deep again as the home side played with huge physicality in the opening quarter.
Vosawai was rattling into contact to lead the way up front while Smith again showed his pace as more turnover ball saw the wing break into space and make big yards for the home side.
Adam Thomas was replaced by Cory Allen, with the centre suffering a cut, while Grenoble got on the scoreboard as scrum half James Hart slotted a penalty. Blues also lost Hoeata before the half hour as he was replaced by Josh Turnbull.
Chris Farrell gave Grenoble go forward with a big run forward while Geraint Walsh cleared danger and then charged down the kick after a great chase. A penalty for holding on gave Patchell the chance to nudge Blues further ahead, but he pulled his kick wide of the target.
Sam Warburton almost picked off an intercept pass after flying out of the defensive line before Hart slotted his second penalty of the half to cut the lead back to six points.
Neat interplay from Evans, Paulo and Thomas saw Blues apply pressure before the break, but loose play on the floor saw ball turned over.
One last attack before the break saw Blues batter down the middle and when the penalty was won for offside it was Patchell who completed the opening 40 minutes with a simple kick for a 15-6 lead at the break.
Blues started the second half in similar vein to the first as the forwards carried ball strongly and punched holes before it was Evans who rolled out of a tackle to finish just yards from the line.
Quick ball was required and Williams immediately fired the ball into the hands of Warburton who powered and stretched over to score.
A high up and under was secured by Smith and with Grenoble struggling to keep up with the pace it was Patchell who had another penalty attempt, but his kick drifted left of the posts.
Blues were looking to open up as Patchell broke the line and quick hands from Williams and Vosawai fed Turnbull into space.
Hart stemmed the flow with a penalty, but the game was still being played in the Grenoble half with Patchell nudging over a kick from close to halfway to extend the lead once more.
The best move of the game resulted in the try bonus point as Vosawai ploughed down field then Williams arched a run to free Dacey. The replacement hooker broke a tackle and fed Patchell on his shoulder and he had the simple job of firing a pass wide to an unmarked Smith to score.
Hammett unleashed his bench in the closing quarter to try and keep the impetus with Allen, Patchell and Dacey again instrumental in try number five before the final pass found Turnbull and he skipped a tackle and strode over.
Grenoble scored a late consolation as Louis Marrou went over in the corner.
09m Patchell t Patchell c 7-0
13m Williams t 12-0
26m Hart p 12-3
35m Hart p 12-6
40m Patchell p 15-6
43m Warburton t Patchell c 22-6
50m Hart p 22-9
56m Patchell p 25-9
59m Smith t 30-9
74m Turnbull t Patchell c 37-9
78m Marrou t 37-14
Cardiff Blues: 15 Rhys Patchell, 14 Richard Smith, 13 Adam Thomas (Allen 23-31), 12 Gavin Evans (Allen 58), 11 Geraint Walsh, 10 Gareth Davies (Fish 73), 9 Lloyd Williams (Knoyle 70), 1 Sam Hobbs (Jenkins 51), 2 Matthew Rees (Dacey 51), 3 Adam Jones (Andrews 60), 4 Jarrad Hoeata (Turnbull 27), 5 Filo Paulo, 6 Macauley Cook, 7 Sam Warburton, 8 Manoa Vosawai (Navidi 70)
Replacements: 16 Kristian Dacey, 17 Gethin Jenkins, 18 Scott Andrews, 19 Josh Turnbull, 20 Josh Navidi, 21 Tavis Knoyle, 22 Cory Allen, 23 Dan Fish