Biarritz Olympique did the necessary required of them with a 32-6 bonus point victory over Zebre at Stadio XXV Aprile.
But they take on group leaders Harlequins at Parc des Sports Aguilera on Friday night with the defeat at Connacht likely to haunt them for some time and their hopes of a quarter-final spot as one of the best runners-up resting in the hands of others.
However, against Italian newcomers Zebre they were never under any great threat - aided and abetted by home full back Paolo Buso being yellow carded in just the fifth minute.
Centre Benoit Baby promptly got their first try and the conversion and two penalty goals from Dimitri Yachvili meant they were scoring at better than a point a minute.
Zebre did respond with a couple of penalty goals from Luciano Orquera but full back Marcelo Bosch crossed for Biarritz's second before the break.
The now customary flood of replacements produced a stop-start affair before Bosch got the scoreboard moving again with his second and Biarritz's third after 56 minutes.
Yachvili's conversion was his last contribution as he joined the substituted players with Seremaïa Burotu collecting the try bonus point for Biarritz with just five minutes to spare.