Bath beat Colomiers 26-17 on perfect conditions at the Recreation Ground, with backrowers Andrew Beattie and Scott Gray scoring tries and the red-hot Ollie Barkley adding 16 points with the boot.
Visiting fly-half Jean-Frederic Dubois kept his side in touch with regular penalty goals, but the French club never looked like recording the necessary eight-point victory, despite leading 11-9 at the halftime break.
Barkley gave the home side an early lead with two penalty goals, but went fromhero to zero went his blindside dart broke down and winger Yannick Larguet toed the ball ahead for 80 metres to give his side a shock lead.
Beattie was driven over in the opening act of the second half and Bath never looked back. Colomiers stayed within range until the 80th minute, when Bath took a quick tap and Gray scored the try that clinched it. The Zurich
Premiership front-runners go through to the Cup quarter-finals with four match points and a 58-42 aggregate victory over the two legs.
At the Stoop, Harlequins went through the motions as they defended a 35-point from their 43-8 victory in the first leg at Montauban.
The English club strode out to a 36-17 victory on the back of a try double to winger Matt Moore and a 11-point kicking haul from first-leg hero Paul Burke.
Montauban were in with a chance at 10-17 at halftime, but the favourites simply moved up a gear and powered away.
Fullback Gavin Duffy's skilful running and solid defence earned him the man-of-the-match award in perfect conditions in front of a 5,000-strong crowd - an impressive turnout given that Quins were virtually through after the first leg.
As well as Moore's double, hooker Ace Tiatia scored his second try in as many games, and he was joined on the try-scoring list by backrower Roy Winters and scrum-half Ben Willis.
Montauban scored tries through hooker David Roumieu and centre Jerome Sieurac, but they were unable to produce the result they needed.