Ronan O'Gara kicked over an early penalty for the visitors before Sean Dougall marked his Heineken Cup debut with a try. O'Gara had no problems with the conversion as the Irish side gave themselves a 10-0 advantage.
The Racing comeback started midway through the first half when Olly Barkley scored his first penalty of the match.
The French club then got themselves level thanks to Maxime Machenaud's try, converted by Barkley.
The former Bath fly-half gave his side a 13-10 lead at the break when he kicked his second penalty of the contest.
Barkley's dominance with the boot continued into the second half as he kicked between the posts again to put his side 16-10 ahead.
Ian Keatley had a chance to get his team back into the contest on the hour, but he put his penalty narrowly wide.
With time running out, Munster winger Simon Zebo ran into space before touching down. Keatley made no mistake this time as his conversion put the visitors 17-16 ahead.
However, Barkley and Mirco Bergamasco both kicked over respective penalties to snatch the victory away from the Irish with just minutes remaining.