The hosts then suffered a setback when Rupert Harden was given a yellow card as Leicester tried to dominate up front. Leicester were subsequently awarded a penalty try after their maul was brought down before the line.
The Tigers looked to be out of sight on the stroke of half time when Peter Betham also got on the scoresheet for the English giants as they built a 22-3 lead.
Jean-Francois Montauriol then saw yellow for taking out Sam Harrison off the ball and, although Leicester were unable to make the one-man advantage count, they did extend their lead later in the second half with another Veainu try.
The visitors capped off the comfortable victory when Greg Bateman scored in the last minute as Leicester made it two wins from two pool games.