Tigers closed the gap on unbeaten Pool Two leaders Toulouse after Julian Salvi's try double underpinned an emphatic first-half display.
Centre Manu Tuilagi and substitute wing Matt Smith also touched down, with fly-half George Ford kicking four conversions, including the extras to a 17th-minute penalty try.
But it proved far from plain sailing as Treviso scored three tries of their own through flanker Dean Budd, prop Lorenzo Cittadini and wing Christian Loamanu, while Alberto Di Bernardo landed two conversions and two penalties.
Leicester led by 19 points at half-time but often struggled to contain Treviso when they attacked from deep, and the second period was distinctly uncomfortable for a Tigers team with strong last-eight ambitions.
Treviso finished easily the stronger team, which does not auger well for Leicester ahead of next Saturday's return fixture at Stadio Communale di Monigo.
And they dare not take their eye off the ball to focus on January assignments with the Ospreys and Toulouse, otherwise their quarter-final hopes could be over before then.
If the group goes to form and pedigree, four-time European champions Toulouse's Welford Road visit next month is likely to decide whether they or Tigers progress as pool winners.
Leicester welcomed back five of the England players on duty in last weekend's stunning victory over world champions New Zealand at Twickenham, with four starting and prop Dan Cole among the replacements.
England lock Geoff Parling skippered a home side which dominated early territory after Ford sent a long-range penalty wide, but Treviso then launched a thrilling counter-attack that was only thwarted by Tuilagi's staunch defensive work.
Treviso full-back Luke McLean and fly-half James Amborisini were architects of the move, but the visitors could not capitalise with points, and Leicester made them pay.
Tigers spurned a kickable penalty after Tuilagi and number eight Thomas Waldrom linked well in attack, opting for a scrum instead, and Parling's decision was justified as the Treviso pack retreated at an alarming rate of knots.
And when they attempted to halt Leicester's charge by illegal means, referee George Clancy had no hesitation in awarding a penalty try that Ford converted.
Tuilagi added a second try eight minutes later after capitalising on a combination of Ford's half-break and poor defence by Treviso centre Tommaso Benvenuti.
Treviso had no answer to Leicester's pace and attacking verve and their third try arrived 10 minutes before half-time after Ben Youngs burst clear from inside his own 22, sparking some pinpoint handling work that ended with Salvi powering over.
Ford again converted, but although Treviso already found themselves in damage-limitation mode, they breached Leicester's defence when Budd touched down one-handed in the corner and Di Bernardo added the extras.
Salvi, though, restored normal service with his second try of the game, securing a bonus point and putting Tigers clear with a 26-7 interval advantage.
Tigers boss Richard Cockerill made two changes at half-time, taking off England hooker Tom Youngs and Fijian wing Vereniki Goneva, but if his team needed a wake-up call it arrived within six minutes of the restart.
Treviso scrum-half Edoardo Gori stormed upfield, scattering Leicester's defence in the process, and the visiting forwards then exerted sufficient pressure for Cittadini to touch down.
Leicester regrouped impressively, though, with Smith rounding off a crisp move after Treviso flanker Simone Favaro was sin-binned for deliberate offside.
Ford slotted his fourth successful conversion and Leicester entered the final quarter 33-14 ahead, but Treviso responded with 11 unanswered points as Di Bernardo kicked penalties either side of Loamanu touching down.
It was a poor second-half display by Leicester and the muted reception from an 18,400 crowd told its own story.
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