After their scrum had won a penalty try, two fine scores from the backs saw Tigers stretch clear in Italy.
Tonga full-back Veainu raced on to Tommy Bell's grubber, before the full-back sent Peter Betham over in the corner to make it 22-3 at the break.
Veainu's solo try earned the bonus before Greg Bateman pin-balled over.
Tongan Veainu may well think he should have had a hat-trick after a spectacular finish in the corner, but the TMO ruled he had knocked on.
In tricky, rain-affected conditions Leicester dominated the opening 40 minutes and with three tries in the bag by the break looked locked on for the bonus point.
But, after Veainu had seen what would have been a superb effort ruled out by the TMO early in the second half, Treviso enjoyed their best spell of the match.
They were on top for 20 minutes, with their scrum finally firing, but could not add to their solitary first-half penalty and Leicester eventually managed to regain control.
An attack from the two-time champions broke down but Veainu - who scored two tries in the World Cup - rescued the ball and beat four men in a confined space with some sizzling footwork to score under the posts.
Replacement hooker Bateman put a gloss on the score as he bounced off several attackers to add a fifth try for Tigers with the last play of the match.
Leicester director of rugby Richard Cockerill: "You've got to be satisfied with maximum points from two games and also with not conceding a try.
"The attitude in defence not to let them in even when we were well ahead said a lot for the team.
"Two wins out of two is a good start, we've got to be happy with that. To get two bonus points is important too - every point will count."
Benetton Treviso: McLean; Nitoglia, Bacchin, Christie, Iannone; Ambrosini, Gori; Zanusso, Gega, Harden, Paulo, Montauriol, Barbini, Minto, Steyn.
Replacements: Pratichetti for Nitoglia (41), Smylie for Gori (71), Muccignat for Zanusso (68), Giazzon for Gega (41), Filippetto for Harden (50), Budd for Paulo (61), Lazzaroni for Barbini (61), de Marchi for Minto (66).
Sin Bin: Harden (17), Montauriol (49).
Leicester: Veainu; Betham, Tait, Smith, Thompstone; Bell, Harrison; Ayerza, T Youngs, Balmain, Barrow, Fitzgerald, Croft, O'Connor, Crane.
Replacements: Catchpole for Smith (70), Bai for Bell (68), B Youngs for Harrison (50), Aguero for Ayerza (66), Bateman for T Youngs (53), Cole for Balmain (57), Slater for Fitzgerald (53), McCaffrey for Crane (50).
Telusa Veainu scored twice to ensure Leicester earned a four-try bonus point from their trip to Champions Cup Pool Four strugglers Treviso.