The English side did all the damage in a first-half that saw them go into the interval leading 20-6. They eventually won the game 20-13.
Barry Everitt got the visitors' off to the perfect start with a nerve settling penalty after four mintues, but Gonzalo Quesada soon responded to level the scores.
Then, midway through the first-half, Irish struck to bag the first of two tries in an impressive opening 40 minutes. A pin-point cross kick found Delon Armitage in space and the right wing ran in a try which Everitt converted superbly.
Quesada replied with a second penalty 10 minutes later, to which Everitt responded, but the Irish landed a hammer blow on the stroke of half-time when a brilliant midfield break by centre Rod Penney was backed up by No 8 Juan Lequizamon, who squeezed over in the corner for another try converted by Everitt.
The visitors lost their way a little in a scrappy second half and they allowed Pau to hit back with a try through Florian Cazalot which Quesada goaled to sneak a bonus point and set-up a nerve wracking final quarter.
Gloucester provided the Premiership with another win in France as they ran in three tries in a 26-10 victory in Bayonne in Pool 3.
England flanker Andy Hazell was in superb form as Gloucester became red-hot favourites to advance to the European Challenge Cup quarter-finals. Hazell was driven over the line for the first halfs only try before young scrum-half Haydn Thomas darted over from close range early in the second half to give the visitors a match-winning lead.
Mark Foster joined the line at a superb angle to score Gloucesters third try, although Bayonne coach Pierre Peytavin was furious at his sides defence after watching four or five players bounce off Foster as he made his way to the line.
But there was no such luck for Gloucester west country neighbours Bristol. They went down 20-13 at Narbonne in Pool 1, nicking a bonus point in the 88th minute with a last gasp Danny Gray penalty that followed an injury time try from Mariano Sambucetti.