Saracens play-maker Thomas Castaignede scored 32 points as his side romped past Rugby Roma into the Parker Pen Challenge Cup draw.
Saracens won 82-5 at Vicarage Road to earn a match with Glasgow after running in 12 tries.
London Irish's Mark Mapletoft scored 13 first-half points to push his side to a 36-24 victory over French club Montauban , who won the first-leg clash.
The English club advance on aggregate to play Narbonne, with Montauban also going through where they join Beziers as lucky losers.
Newcastle booked a second round European Parker Pen Challenge Cup tie against Montferrand next month with a 66-27 rout of outclassed Spaniards Valladolid.
Italian side Viadana upset French rivals Brive 38-22, but Brive go through after their first-leg 39-3 victory.
In Saturday's action Harlequins cruised into the next round with a thumping 63-3 victory over Cetransa El Salvador at The Stoop.
The Londoners took a 31-18 advantage into their first round second leg tie against the Spanish youngsters and easily reached the next stage.
Bath followed up last weekend's 75-11 victory at L'Aquila with a comfortable 50-0 win at the Recreation Ground.
Connacht survived a determined Beziers display to squeeze into the second round of the Parker Pen Challenge Cup despite their defeat.
Beziers scrapped their way to a 13-11 win in Ireland but Connacht's first-leg triumph in France was enough to see them progress courtesy of a 29-23 aggregate win.
In Italy, Petrarca held Colomiers to a 12-8 lead at half-time, but two tries to visiting winger Farid Sid ended their hopes and the French heavyweights romped to a 38-20 victory to add to their 37-12 first-leg win.
Pau also advanced after a comfortable 25-6 win against Parma which saw them through 58-34 on aggregate.
On Friday, Glasgow became the first British side to qualify for this season's Cup with a 38-13 home victory over Montpellier.
The French side were never in it as the Scots, who took a 19-point margin into the match, made up for the disappointment of not being in the Heineken Cup.
Rotherham's woes continued as they crashed 35-13 at Narbonne.
The Yorkshire outfit were seven points behind after the first leg, but were never in it as their French rivals scored four tries to Rotherham's one.