A late try by prop Hoani Tui gave Exeter Chiefs a hard-fought 17-6 victory over Bourgoin in Amlin Challenge Cup Pool Three.
Tui crashed over three minutes from time following Tom Johnson's earlier score to seal victory for Rob Baxter's side.
Bourgoin had threatened a comeback after two penalties by former Leeds fly-half Alberto Di Bernardo, who also missed two more kicks.
But Exeter had the last say at Sandy Park and a win at Montpellier next week will see them reach the quarter-finals of a European competition for the first time.
Tries: Johnson, Tui
Pens: Di Bernardo 2
Bayonne left themselves facing an uphill struggle to qualify from Pool One as they lost 35-21 at home to Connacht.
Fly-half Ian Keatley did the damage for the Irish side as he slotted six penalties and a conversion for a personal haul of 20 points, while a penalty try and scores from Brian Tuohy and Fionn Carr completed their scoring.
Thibault Lacroix and Marc Baget crossed for Bayonne but they now need a bonus point win at Harlequins next weekend if they are to have any chance of advancing to the last eight.
Tries: Lacroix, Baget
Pens: Audy 3
Tries: Tuohy, Carr, Penalty try
Pens: Keatley 6
Yellow cards:Sebastien Fauque (Bayonne), Andrew Browne (Connacht)
Gloucester won 55-7 at Rovigo to keep alive their hopes of a place in the quarter-finals.
Henry Trinder, Charlie Sharples and Tim Taylor all scored twice as Gloucester ran in eight tries at Stadio Mario Battaglini.
Taylor also converted three tries while Matt Cox and Jonny May also crossed and Freddie Burns added nine points with the boot to cap a comfortable win.
That closed the gap on pool leaders La Rochelle to three points though the French club will deny Gloucester a place in the last eight with victory next weekend.
Trinder opened the scoring, pouncing on a slip in the Cavalieri defence, for his first before stepping through from Burns' pass for his second.
Number eight Cox powered through for the third, Sharples charged in off his wing to claim the bonus point and then grabbed a second from Olly Morgan's off-load.
The game stalled in the second half before Gloucester rallied late on with three tries in the final seven minutes for Taylor (two) and May.
Tries: Hazell, May, Sharples 2, Taylor 2, Trinder 2
Cons: Burns 3, Taylor 3
Harlequins ran in six tries in a comfortable victory against European newcomers Cavalieri Estra Pool One.
The result in Italy leaves Quins four points clear of group rivals Bayonne, who thet face next week in a decisive clash.
Maurice Fa'asavalu scored the first try after 12 minutes and Danny Care followed as Harlequins led 20-6 at the break.
The second half was more impressive from the Aviva Premiership outfit as they wrapped up a bonus-point win with a further four tries.
Sam Smith scored two early second-half tries, Cavalieri's Wouter Moore and Tom Casson then traded scores before Karl Dickson went over on the stroke of full-time.
Pens: Wakarua 3
Tries: Casson, Care, Smith 2, Fa'asavalu, Dickson
Cons: Clegg 6
Pens: Clegg 2
Yellow card:Gabriel Bocca (I Cavalieri Estra)
Elsewhere, Crociati were 16 - 12 winners at home to Bucharest Oaks.
Try: Penalty try
Pens: Anversa, Iannone 2
Pens: Dumbrava 4
Yellow cards:Marian Drenceanu (Bucharest Oaks), Mihai Macovei (Bucharest Oaks)