Wing Tomas De Vedia scored four tries as Saracens put Narbonne to the sword
and secured their place in the European Challenge Cup quarter-finals.
The 47-20 win puts Alan Gaffney's men back on top of Pool Two, giving them a guaranteed spot in the final eight.
But they will be looking for a win at Glasgow, who remain in contention, next Friday to ensure a home quarter-final.
Sarries scored seven tries in all, while Glasgow ran in six in their 47-17 rampage past Italians GRAN Parma.
Sam Pinder and Rory Lamont both crossed twice, while Dan Parks landed 17 points with the boot.
Worcester's hopes of qualifying for the last eight took a knock after they lost 35-22 to Clermont Auvergne at Sixways.
The Warriors will need a big win over Viadana next week to give themselves a chance of sneaking into the quarters as one of the three best runners-up.
John Brain's side paid the price for a dreadful start to the match, conceding 20 points in as many minutes.
On Friday, Bath took a big step towards the quarter-finals with a 36-24 win in Connacht but Premiership leaders Bristol lost to the Dragons.
Andy Beattie, Olly Barkley and Michael Stephenson (three) scored Bath's tries.
Bristol went down 17-11 to trail Dragons on points difference, while Harlequins beat Montpellier 37-27 but stay second behind Bath in pool four.
Newcastle beat leaders Brive 24-17 at Kingston Park to keep their hopes of topping the group alive.
The Falcons were hammered 41-12 by the French side earlier in the season but they emerged winners in difficult conditions.
Bath moved to 21 points at the top of the pool, and need only a point against bottom-placed Montpellier at the Rec next weekend to secure a place in the quarter-finals.
Harlequins are probably playing for a best runners-up spot in their home match against Connacht in the final round.
Newport-Gwent Dragons face a tough trip to Bayonne in the final round, while Bristol entertain Romanian side Bucuresti, who lost 38-31 to Bayonne on Friday.