The Blues opened powerfully at the Centro Sportivo San Michele, influential flanker Molitika rampaging through weak Italian tackling for an early try.
A controversial touch-judge intervention saw Deiniol Jones sin-binned for a high tackle, allowing Gerard Fraser to get Calvisano on the scoreboard with a penalty.
That was cancelled out by a Blair kick, before a strong Gary Powell charge to the line set up the visitors' second try.
The recycled ball came back to man-of-the-match Robinson, who chipped through for brother Jamie to chase.
The centre was hauled back as he went for the touchdown under the posts, a penalty try resulting.
As the Blues looked to take control they were struck a double blow, first as burly Australian number eight Purll threw an outrageous dummy on the visitors' 22 before storming in under the posts.
Shanklin was out to make an impression on his recall to the side
As he crossed, a flag was spotted by the referee who took the touch judge's advice before sin-binning Jamie Robinson, leaving the incredulous Blues down to 14 men for the second time.
Blair helped compose his side with his second penalty, although that was cancelled out by Paul Griffen just before the break.
Again the Blues came quickly out of the blocks, a long Rhys Thomas line-out throw on the 22 reaching Spice.
The scrum-half broke the cover defence to cross, Blair's conversion stretching the lead to a comfortable 25-13.
The crucial bonus-point try soon followed, a long Nicky Robinson pass sending Rhys Thomas on an outside arc, before the hooker off-loaded inside to Shanklin who celebrated his Blues recall with a try.
With Blues confidence flying, Calvisano failed to handle the Welsh side's off-loading game, a superb Nicky Robinson inside pass to Blair securing the fifth try.
Shanklin sparked the try of the match from his own half, a dazzling back-line move seeing the ball go through the hands of Blair and Martyn Williams before the flanker sent Nicky Robinson under the posts.
The home side hit back with a well-worked line-out move down the blind-side, hooker and captain Ghiraldini nipping over.
It was slight relief, Shanklin and Williams again in rampaging form as Halfpenny was sent over, before Gareth Thomas scrambled a try.
The Blues will be satisfied with their Heineken start and record score in the competition, but know that sterner tests await with Gloucester at the Millennium Stadium next Sunday and Biarritz also in pool six.
Blues coach Dai Young:
"After a good start we blew a few first-half opportunities and lost our way a little, so we wanted a big 20 minutes after the break and we really stepped up the intensity and accuracy.
"Confidence is a huge thing, you need momentum to play well and we did that.
"We're obviously pleased, we answered our critics - and we've had a few. The attitude from one to 22 was excellent."
Calvisano coach Marc Delpoux:
"Cardiff were bigger, stronger, have better organisation, players, structure and more money so what we saw here was the picture of that difference.
"I was happy with the effort in the first half but then we collapsed because we are still not ready to compete at this level for 80 minutes."
Rugby Calvisano: McLean, Forcucci, A. Pratichetti, M. Pratichetti, Nitoglia, Fraser, Griffen, Tui, Ghiraldini, Evans, Bernabo, Sidoli, Zanni, Persico, Purll. Replacements: Stanojevic for McLean (59), Raineri for Fraser (35), Patelli for Griffen (75), McKenzie for Tui (52), Moreno for Evans (59), Dal Maso for Sidoli (41), Zaffri for Persico (64).
Blues: Blair, Halfpenny, J. Robinson, Shanklin, G. Thomas, N. Robinson, Spice, Jenkins, T. Thomas, G. Powell, Jones, Tito, Molitika, M. Williams, A. Powell. Replacements: Sweeney for N. Robinson (67), Rees for Spice (53), Filise for Jenkins (64), Morgan for Tito (53), Sowden-Taylor for Molitika (53). Not Used: G. Williams, J. Roberts.
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