Irish had tries from Jonathan Joseph and Marland Yarde and seven points from the boot of Steve Shingler.
Gautier Gibouin scored Bordeaux's try with Nicolas Sanchez converting.
Gloucester made it six from six in Pool One as they ran in five tries in their 36-16 home win over Mont-de-Marsan.
Jonny May and Henry Trinder both crossed over twice while Charlie Sharples also contributed a try in the 22nd minute.
England hopeful Billy Twelvetrees came off the bench to grab two penalties and a conversion with Freddie Burns also kicking three points.
Scotland international Jack Cuthbert helped himself to a hat-trick as Bath made it six out of six in Amlin Challenge Cup Pool Four with a routine 53-8 victory over Bucharest Wolves at the Recreation Ground.
The home side became the first team to post a perfect record in the pool stage this season as they piled on the points to underline their qualification for the quarter-finals.
They scored nine tries in all, with Cuthbert crossing twice in the opening half to give his side a 24-3 interval lead.
Tom Dunn, Horacio Agulla, Nick Kosta, Chris Cook, Will Skuse and a penalty try provided the other scores with Tom Heathcote booting three conversions and Sam Vesty also adding two points.
Worcester ran in 11 tries in a 71-19 win over Spanish champions Bizkaia Gernika in Amlin Challenge Cup Pool Two.
Outside-half Danny Gray helped himself to 21 points with eight conversions and a try.
Errie Classens, Nikki Walker and Josh Drauniniu scored a brace each with Jake Abbott, Blair Cowan, Aleki Lutui and Ben Howard also crossing.
Bizkaia replied with a Santi Salas try and 14 points from the boot of Declan Cusack.
Stade Francais became the second French side to advance to the quarter-finals as they finished on top of Pool Five with a 39-17 win over London Welsh in Valenciennes.
The 2011 finalists ran in six tries to overtake Grenoble at the top of the table to clock their 17th win in their last 19 home games in the tournament.
The Exiles took the lead with a third-minute penalty from scrum-half Alex Davies, but found themselves trailing 18-3 at the break after the home side ran in three tries. The bonus point was clinched six minutes into the second half with a penalty try.
The visitors conceded one try at the end of the first-half when number eight Alfie To'oala was in the sin bin and then two at the start of the second period when fellow back-row man Lee Beach also saw yellow.
But the Exiles rallied to score two tries in the space of five minutes by right wing Phil Mackenzie, both converted by Davies, to cut the gap to 15 points midway through the second half.
In the end, though, Stade Francais wrapped up the game with their fifth try from Francis Fainifo six minutes from time.
Elsewhere, in Pool 3 Bayonne won 52-0 at Rugby Mogliano to finish second to Wasps in the group.