Leeds ran in seven tries against Calvisano - including a hat-trick for full-back Leigh Hinton - although there were glimpses of the visitors' potential, and next weekend's return match in Italy is likely to be closer.
Leeds winger Tom Biggs was over the try-line after only four minutes, and Hinton's effort moments later prompted home fans to settle back for an afternoon of one-sided rugby action.
Back row John Dunbar was the next player on to the scoresheet, and the boot of former Italy A fly-half Alberto Di Bernardo was adding to the visitors' woes as they went into the half-time 19-0 down.
Calvisano winger Daniele Forcucci scored shortly after play resumed to keep the match interesting, but lock Stuart Hooper's powerful touchdown and Hinton's second try ended any faint hopes of an Italian comeback.
Replacement hooker Vili Ma'ami bagged Leeds' sixth try, and there was just time for Hinton to complete his hat-trick.
In the final Challenge Cup match of the weekend, Brive spiced up Newcastle's Pool 3 with a 71-0 victory over Centransa El Salvador at Stadium Municipal.
The bonus-point win gives Brive 10 points from the opening three rounds, the same number as the Falcons and one ahead of Connacht.
Brive ran in 11 tries against the hapless Spanish club, with a hat-trick for centre Fabrice Estebanez and two tries each for Welsh full-back Barry Davies and wingers Alexis Palisson and Farid Sid. Former England hooker Steve Thompson also made it on to the scoresheet.