Tries from Toby Flood, Aaron Mauger, Jordan Crane and Matt Smith ensured Leicester took the maximum five points, while despite scoring three tries of their own, Perpignan left with nothing.
Commercial commitments meant All Black fly-half Dan Carter could only watch from the stands as his new team-mates fell to their second successive loss in the competition following a 15-9 reverse at the hands of the Ospreys in October.
Carter had originally been expected to make his first start in a Perpignan shirt at the home of the English giants but he will now have to wait until next Sunday's return fixture to experience his first taste of northern hemisphere rugby.
Leicester fly-half Flood, in his first season of Heineken Cup rugby having moved from Newcastle Falcons during the summer, contributed a total of 23 points as he added four penalties and three conversions to his 19th-minute try.
Flood took advantage of a gaping hole in the Perpignan midfield to open the try-scoring for the hosts after earlier kicking the Tigers into a 6-0 lead. Impressive handling from forwards and backs saw the Tigers keep the ball alive until Perpignan finally ran out of defenders. Flood allowed the drift defence to move past him before dancing through the gap between the 10 and 12 channel for his fifth try in Leicester colours.
A breakaway converted try from Maxime Mermoz and two penalties from David Mele had seen Perpignan level the scores as the first period drew to a close but Leicester went into the break with a seven-point lead thanks to Mauger's well-worked try with the last play of the half. The former New Zealand international cruised over from first receiver after a bludgeoning run from centre partner Dan Hipkiss had taken play to within two metres of the Perpignan line.
Flood added the extras before kicking two further penalties in the second period as Heyenke Meyer's side stretched further ahead, but the visitors refused to give in. A second try from flanker Ovidiu Tonita brought them closer before Crane and Smith effectively killed the game as a contest.
Crane's score was a throw back to the Leicester of old as the pack pushed their French opponents over their own line from a scrum 15 metres out, while Smith's well-taken effort hinted at the possibilities when the Tigers move the ball wide.
Right wing Smith, a Tigers Academy product and son of former Leicester coach and skipper Ian 'Dosser' Smith, has been named in every matchday squad so far this season and is currently keeping England wing Tom Varndell out of the starting XV.
The 23-year-old supplied an assured finish to give the Tigers a hard-fought bonus-point win and, although Perpignan had the last word through a penalty try with the final action of the match, it was Leicester whose European hopes remain very much alive at the halfway mark of the pool stages.