Northampton ran in 10 tries as they routed Bristol 66-3 at Franklin's Gardens in Pool Two.
Winger Chris Ashton scored a hat-trick of tries while Paul Diggin and Mark Easter both scored twice.
Bruce Reihana, Roger Wilson and Jon Clarke also added scores in a one-way contest where Saints earned a bonus point by the interval.
Elsewhere, Newcastle Falcons defeated Overmach Parma 20-14 and Saracens overcame Bayonne 16-6.
The Falcons had teenager Rob Miller to thank for their win in Italy.
Tries from Danny Williams and John Rudd secured the win but 19-year-old Miller kicked 10 points.
The win keeps Newcastle's quarter-final hopes alive one point behind Brive in Pool Four, as Miller booted two penalties and two conversions.
Saracens held onto top spot in Pool Five with a hard-earned victory at Stade Jean Dauger.
Replacement Mosese Rauluni settled a tight encounter with the game's only try four minutes from time.
Tempers had flared amid the stalemate when props Census Johnston and Julian Fiorini were sin binned for punching early in the second half.
Meanwhile in Pool One,
Connacht earned a bonus-point win in Italy as they beat Rovigo 35-20.
London Irish made it three wins out of three in the European Challenge Cup after recording a six-try 38-0 demolition of French side Dax.
The Exiles never looked back after Sailosi Tagicakibau crossed in the third minute.
Tagicakibau and Alfredo Lalanne both scored twice, while Shane Geraghty and Elvis Seveali'i also crossed the line.
Worcester are just one point clear at the top of Pool Three after losing 29-14 to Bourgoin in France.
The Warriors had already won in Italy and Romania and despite All Black star Rico Gear in their line-up, they failed to claim a hat-trick of away successes.
Tries in either half from centre Alex Grove and hooker Aleki Lutui were not enough to lift the mood on a disappointing night for Mike Ruddock's men.
Warriors' director of rugby Mike Ruddock told BBC Hereford and Worcester: "We possibly made too many changes due to the injuries that we had, but we are not looking for excuses.
"Bourgoin deserved their victory - they beat Castres away last week so they are obviously in good form and they were industrious, busy and took the couple of chances that came their way.
"But if we are honest, it was our poor play that let them in."