Lachie Munro gave the hosts the lead with a couple of penalties before Chris Hala'ufia drove over for the first try of the night.
Ian Humphreys converted to put Irish ahead and Topsy Ojo then went hurtling over for Irish's second score.
Again Humphreys added the extras and Exiles continued to dominate possession and territory for the remainder of the half.
They extended their advantage early in the second period with a penalty from Humphreys before Halani Aulika dived over for his third try of the season.
The sin-binnings of Bordeaux forwards Rohan Kitshoff and Fabien Rofes did little to help the home side and they found themselves further behind when Sailosi Tagicakibau finished off an overlap in the corner.
A second try for the Samoan extended Irish's advantage and Jonathan Joseph rounded off the scoring when he raced clear for an 80-metre intercept try.
The visitors did concede a late score with debutant prop Richard Palframan sin-binned, but it failed to mar a fantastic evening for Brian Smith's men.
Exiles now look forward to a visit from Mont-De-Marsan in the second round of the Amlin Challenge Cup on Saturday (3pm ko).
The French side were beaten 11-6 at home by Gloucester in their opening match.