Boss Phil Davies had warned his Blues that they would have to match the intensity and physicality of the Chiefs, but an inspired first half from the hosts saw them pull clear in emphatic fashion.
England flanker Tom Johnson opened the scoring before a staggering five-minute spell from the Chiefs saw them all but wrap the game up in simply scintillating fashion.
Quick-fire tries from home captain Dean Mumm and Matt Jess had Exeter in complete control of the Pool 2 clash.
The bonus point was wrapped up by flying wing Fetu’u Vainikolo inside 30 minutes as he stepped inside one man and took advantage of slip to tear over the whitewash.
Flanker Ben White grabbed try number five before the interval as irresistible Exeter opened up a 36-3 lead after a quite stunning opening 40 minutes from the hosts.
Lloyd Williams and Robin Copeland went over for Blues in a frantic second half while Ian Whitten responded for Chiefs before being yellow carded alongside team-mate Sireli Naqelevuki as Exeter were forced to play with 13 men for a spell.
Blues made the numerical advantage count ruthlessly as Alex Cuthbert grabbed a third try and the fourth - and with it vital try bonus point - was taken by Harry Robinson to ensure then visitors took something from the game.
Exeter started the game at a real high tempo with big Number Eight David Ewers handing off two men in midfield as the Chiefs went left and right with pace and intent before knocking on down the left wing.
The home side looked to control territory in the opening minutes before Blues were eventually able to make some ground as a high kick from Rhys Patchell almost fell kindly for wing Harry Robinson.
Cory Allen nearly picked off a wide floated pass, that would have seen the young centre streak away, but the ball was just behind him and he failed to gather after instinctively shooting out the defensive line.
Exeter opened the scoring on nine minutes after an initial lightening burst fromVainikolo down the middle saw him break the defensive line and feed Matt Jess on his right shoulder.
The home forwards kept driving on towards the line and eventually the Blues defence was breached as Johnson barged over bodies to dot down from close range. Gareth Steenson saw his conversion attempt bounce back off the post.
Dafydd Hewitt won a penalty, as Exeter were guilty of holding on in the tackle, and Leigh Halfpenny reduced the lead with a well struck effort that split the posts. Four minutes later the same result followed when Steenson drilled over a confident kick.
Halfpenny showed all his rugby skills and awareness with a superb low drilled kick after a rare poor effort from Steenson was gobbled up by full back and returned with interest.
A charged down clearing kick by lock Filo Paulo was then taken on the charge by Patchell and when Blues went wide it was Alex Cuthbert who looked to run around the last man before the attack broke down.
Exeter looked ominous with every attack from deep as they made Blues work exceptionally hard to keep any ball and keep making tackles.
The visitors then lost a crucial lineout inside the 22 and Exeter struck in a flash. Blues looked to hold firm after wave after wave of home pressure before skipper Mumm picked up at the base of a ruck and burst straight down the middle to beat Halfpenny’s tackle and crash over.
Two minutes later it went from bad to worse as Exeter again broke tackles from deep and with support runner after support runner on the shoulder they sliced through with Jess this time weaving his way over.
Exeter were now simply unstoppable and the fourth try and bonus was secured in simply devastating fashion as again they went wide and this time it was the impressive Vainikolo who used his pace and direct running style to fly over.
Shell-shocked Blues looked to respond to the home team’s incredible ten-minute spell as a period of aerial interplay between both sides finally saw the visitors go wide and try to exploit an overlap.
Cuthbert and Andries Pretorius took ball on but when it was shipped inside the difficult pass was spilled forward by Patchell as he looked to break clear.
The home super show resumed three minutes before the break as Exeter again broke tackles as the rattled into contact and after they ominously rumbled up to the line a fifth try was taken by back row White who exploited numbers around the fringes to dive in.
Cardiff won a penalty at the start of the second half and with such a big deficit to overturn kicked to the corner to try and set up an attack. The lineout was won but after looking to break through the ball was lost forward in the tackle.
An arching run from Cuthbert finally saw Blues break into space and he fed Bradley Davies who was hauled down by Vainikolo. The visitors looked to land a blow but after Robinson and Matthew Rees took ball on a pass from Patchell was intercepted and Exeter were away.
Davies made a trio of changes to try and inject a fresh spark into his team, but seconds later Exeter were over again as neat handling and an inside step from Steenson sent Ian Whitten over.
Cardiff Blues finally struck a blow when Exeter looked to run the ball from deep but were guilty of losing it on the floor and Lloyd Williams pounced to race over unopposed.
Robin Copeland and Allen gave Blues more go forward as they looked to mount a recovery in the face of huge home pressure and intensity.
Exeter again pressed the self-destruct button at the breakdown deep in their own half as another ball popped out and this time it was Copeland who took the loose ball and showed his pace.
The home side were suddenly struggling to contain a Blues team playing with freedom all over the field as a deliberate knock on by Whitten, as the visitors looked to play, saw him yellow carded.
Seconds later Chiefs were down to 13 men as Naqelevuki was yellow carded for a high tackle on Robinson.
Blues scored a third try of the afternoon when Cuthbert went over in the corner after the visitors exploited an overlap. It was a great finish by the Wales winger who crashed over under massive pressure and was given the score after the officials consulted the TMO.
Blues were now in sight of a try bonus that seemed unlikely at the break and more neat interplay saw them break into clear space only to be pulled back by referee Jerome Garces for a forward pass.
The fourth try and try bonus came on 72 minutes, just seconds before Whitten returned, as more neat hands and a pass out of the tackle from Copeland saw Robinson blast away down the left for the point.
Exeter stemmed the flow of points with a penalty from Henry Slade while Lewis Jones almost marked his introduction by skipping out of tackles towards the try line.
A late yellow card for replacement Marc Breeze had little impact as Blues were forced to take a point from the opening game of the tournament.
09m Johnson t 5-0
13m Halfpenny p 5-3
17m Steenson p 8-3
25m Mumm t Steenson c 15-3
27m Jess t Steenson c 22-3
30m Vainikolo t Steenson c 29-3
38m White t Steenson c 36-3
53m Whitten t 41-3
55m Williams t Halfpenny c 41-10
59m Copeland t Halfpenny c 41-17
67m Cuthbert t 41-22
72m Robinson t Halfpenny c 41-29
76m Slade p 44-29
Cardiff Blues: 15 Leigh Halfpenny, 14 Alex Cuthbert, 13 Cory Allen, 12 Dafydd Hewitt, 11 Harry Robinson (Smith 77), 10 Rhys Patchell (Davies 75), 9 Lloyd Williams (Jones 75); 1 Gethin Jenkins (Hobbs 74), 2 Matthew Rees (Breeze 77), 3 Taufa’ao Filise (Andrews 52), 4 Bradley Davies, 5 Filo Paulo (Reed 52), 6 Josh Navidi, 7 Sam Warburton, 8 Andries Pretorius (Copeland 52)
Replacements: 16 Marc Breeze, 17 Sam Hobbs, 18 Scott Andrews, 19 Lou Reed, 20 Robin Copeland, 21 Lewis Jones, 22 Gareth Davies, 23 Richard Smith
Exeter Chiefs: 15 Phil Dollman, 14 Matt Jess, 13 Ian Whitten, 12 Jason Shoemark (Naqelevuki 58), 11 Fetu’u Vainikolo, 10 Gareth Steenson (Slade 56), 9 Dave Lewis (Thomas 48); 1 Brett Sturgess, 2 Chris Whitehead (Yeandle 49), 3 Hoani Tui (Rimmer 52), 4 Dean Mumm, 5 Damian Welch, 6 Tom Johnson (Horstmann 28), 7 Ben White, 8 David Ewers
Replacements: 16 Jack Yeandle, 17 Ben Moon, 18 Carl Rimmer, 19 Don Armand, 20 Kai Horstmann, 21 Haydn Thomas, 22 Henry Slade, 23 Sireli Naqelevuki