Owen Farrell played a key role with a try, four conversions and three penalties for a personal points tally of 22 points, while David Strettle, Chris Wyles, Ernst Joubert and debutant John Smit also crossed for the hosts.
Treviso, who trailed 16-3 at half-time, claimed two late tries through replacements Franco Sbaraglini and Gonzalo Padro but it was too little too late for the Italian side.
The only real setback for Sarries in their opening game in Pool Five was an injury to flanker Justin Melck, who was hurt during a collision at the breakdown a minute after coming on for a blood injury to Andy Saull.
The game was held up for 10 minutes before Melck was taken from the field on a stretcher, although by that stage Farrell had already booted them in front.
However the lengthy break stopped their momentum, with Farrell doubling their advantage after 20 minutes with his second penalty.
A try was not long in coming, though, as a kick from Charlie Hodgson was not dealt with by Treviso's Ludo Nitoglia, the full-back failing to ground the ball over his line, allowing Farrell to pounce for a gift.
The centre added the conversion to make it 13-0, but Saracens found themselves down to 14 men soon after when Schalk Brits was adjudged to have made a late tackle and was sent to the sin-bin.
Treviso made the most of the extra man to get on the scoreboard, fly-half Willem de Waal slotting over a penalty.
Farrell then missed successive penalty attempts, the second after Diego Vidal was sin-binned for making an illegal block on Neil de Kock, before successfully converting one from 40 metres out just before half-time.
The Aviva Premiership side then turned up the heat from the re-start and were rewarded with their second try after 47 minutes.
Hodgson's pass from a ruck was then being switched back inside by Brits to scorer Strettle, who had made a terrific diagonal line off his right wing.
Smit came on to make his Sarries debut on 58 minutes, the former South Africa World Cup-winning captain replacing compatriot Brits.
Not long after Sarries crossed again, James Short making the initial break before USA full-back Wyles raced around the outside on the right to score.
The bonus point was secured four minutes later when Joubert scored on the left after a long pass left by Ben Spencer, Farrell adding the third of his four conversions.
Treviso kept battling and crossed themselves after 74 minutes, Sbaraglini touching down on the left, though Sarries replied when new boy Smit drove himself over from a ruck.
There was still enough time left for Padro to score a second for Treviso, Willem De Waal adding his second conversion with the game's final kick.
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