Needing just a point to safeguard their passage through to the knockout stages, the English heavyweights laboured against the Italian outfit and had to erase a 17-13 half-time deficit before pulling clear in the second half.
Mouritz Botha and David Strettle both touched down for Sarries and Owen Farrell added 16 points with the boot to set up a home quarter-final tie.
Mark McCall's men are now the only English side left in contention in Europe's top tournament, but will know that they will have to up their game several notches when the knockout stages commence in early April.
They came into the match hoping for a bonus point win to seal top spot in Pool Five and a home quarter-final, but Treviso, unbeaten in their previous two pool games at home, were in no mood to lie down.
Farrell struck first blood for the visitors with a penalty after 10 minutes but they were rocked on their heels when Robert Barbieri dotted down for the opening try moments later, which was converted by Kris Burton.
Sarries responded impressively and hit back with a try of their own, Botha barging over from close range after the Saracens forwards had pummelled the home pack.
Farrell made no mistake with the conversion but again the visitors were found wanting in defence, and conceded a second try more or less off the restart.
Barbieri was once again instrumental, punching a massive hole in the Saracens midfield before the ball was spun wide to Tommaso Iannone, who touched down in the corner.
Burton added the conversion, and then an opportunistic drop goal to leave Treviso with a 17-10 lead 25 minutes in.
Things went from bad to worse from Saracens after they lost both Kelly Brown and Steve Borthwick to injury in quick succession, and with pool rivals Biarritz by this stage 17-0 up against the Ospreys, the wheels were in serious danger of coming off.
Farrell reduced the deficit to four points just before the break, but at half-time Saracens' cup prospects were still looking touch and go.
Thirty seconds into the second half, however, the game took a seismic swing when Strettle blocked down an attempted clearance and strolled his way over the line for a gift-wrapped try.
Farrell converted and then traded penalties with Burton to keep his side just ahead at 23-20.
Irish veteran Peter Stringer then came to the rescue for Saracens, somehow holding up Antonio Pavanello when Treviso looked certain to touch down for a third time.
Tobias Botes, meanwhile, looked to have scored a perfectly good try, but it was mysteriously overruled by stand-in referee John Carvill, who had replaced the injured Alain Rolland in the first half.
Saracens at this stage were hanging on by their finger nails, but the accuracy of Farrell allowed them to keep the scoreboard ticking over, another three-pointer on the hour mark stretching the lead to six points.
Rather than kicking on in search of the bonus point which would have guaranteed their status as third seeds, Saracens spent most of the final quarter on the back foot simply trying to protect their lead, which they just about managed to do.
Speed king Takudzwa Ngwenya scored a blistering hat-trick of tries as
Zimbabwe-born United States international Ngwenya, regarded as one of the fastest men in world rugby, was in superb form during a one-sided rout against opponents unable to deal with his pace.
It was easy work for twice-European finalists Biarritz and they profited against a flimsy Ospreys defence to wrap up their Pool Five campaign with a bonus point triumph.
Left-wing Benoit Baby and impressive former England full-back Iain Balshaw got their other touchdowns with scrum-half master tactician Dimitri Yachvili racking up 11 points through four conversions and a penalty.
Swansea-based Ospreys, who started the match in second spot in Pool Five but level on 13 points with their third-placed opponents, had the dominant scrum but little else with their only score coming when replacement hooker Richard Hibbard pounced on a Biarritz line-out blunder for a try.
France star Yachvili twice cut open Ospreys' defence to set up Biarritz's first try with just five minutes on the clock.
The ball was worked to Ngwenya and he made light work of a potentially difficult finish by brushing aside Dan Biggar and Eli Walker.
Balshaw created the home side's second try second after launching an attack from inside his half.
He drew Ospreys full-back Barry Davies before freeing Ngwenya. Ireland star Tommy Bowe dashed across from the other wing in a valiant effort to cut the flyer off but was unable to prevent the touchdown.
Yachvili again expertly converted from wide out to put them 14 points up against opponents who appeared shell-shocked. Even after doing something right, like winning a penalty with a strong scrummage, Ospreys kicker Biggar failed to find touch.
Biarritz ran the ball back and the movement culminated with flanker Justin Tipuric infringing at the breakdown for Yachvili to slot the penalty to make it 17-0.
The Welsh region made changes at half-time with Ryan Jones taking over from Tom Smith at blindside flanker, Ryan Bevington from loose-head prop Paul James and Kahn Fotuali'i from Rhys Webb at scrum-half.
But Samoa star Fotuali'i had been on for barely five minutes before unluckily being sin-binned for an alleged dangerous tackle on Wenceslas Lauret.
Lauret had chased and jumped to catch the ball and Fotuali'i was unable to get out of his way.
The Biarritz player made a meal of it and English referee Wayne Barnes quickly stuck a hand in a pocket and brandished the yellow card.
While a bemused Fotuali'i was kicking his heels on the sidelines a long pass from Biarritz outside-half Julien Peyrelongue missed out two attackers to put Baby over in the corner for an unconverted try.
He was still a spectator when Balshaw managed to ground the ball in the corner for a touchdown to secure a bonus point.
Hibbard got Ospreys on the score-board but the one-way traffic resumed when Ngwenya waltzed through a reluctant defence for his third try to put the gloss on a compelling performance.
Munster v Ulster
Leinster v Cardiff Blues
Edinburgh v Toulouse
Saracens v Clermont Auvergne
Saracens/Clermont Auvergne v Leinster/Cardiff Blues
Munster/Ulster v Edinburgh/Toulouse