A try four minutes from time was all that robbed Connacht of their second win on French soil this season after a bruising encounter in the wind and rain at Stade de Hameau in Pau.
Connacht defense held firm in the face of a typically physical French onslaught and now go on to meet Narbonne in the quarter-finals after they saw off the challenge of London Irish also on Saturday night.
The first leg will take place in Narbonne next Saturday at 7.30 pm, with the return leg in the Sportsground the following Saturday (Jan 31st) at 2 pm.
Connacht took the game to Pau from the outset, and led 6-0 at half-time thanks to penalties from Eric Elwood after 20 and 36 minutes.
Pau, now backed by the wind, came out fighting in the second-half and registered a try from French international Damien Traille after 49 minutes.
Connacht batted down the hatches after that with some ferocious tackling which kept Pau at bay and they looked set for another win until sub Rida Jauquher struck for a late try.
But it was never going to influence the tie with Connacht safey marching through to the quarter-finals with a double scores aggregate victory.