Tries from Juan Jose Imhoff and Eddy Ben Arous either side of the interval proved the difference as the Scottish outfit remained winless in the competition.
Edinburgh stay bottom of Pool One, with no points to their name, but they restored some pride with the committed performance. It took them just two minutes for them to open their account in Paris as Greig Laidlaw dissected the posts.
Racing hit back through the boot of Olly Barkley on 10 minutes. Michael Bradley's men continued to waste scoring opportunities as Laidlaw fired two penalties in quick succession wide and the French club punished their Scottish rivals for their lack of killer instinct with the game's opening try.
Fabrice Metz made the initial inroads and some slick handling released Imhoff, who danced around Tom Brown to score.
Barkley failed to add the extras, but the try handed his side an unlikely 8-3 lead.
Racing were buoyed by their score and came close to grabbing a quick-fire second following a sustained period of pressure, but Edinburgh survived.
But they were still unable to take advantage of point-scoring opportunities as another Laidlaw effort fell short before he made some amends with the final kick of the half.
Edinburgh were once again the better side in the opening exchanges following the restart, but they were unable to turn pressure into points.
They opted for the corner as they looked to force a try, but lost possession and conceded a penalty as Racing escaped unpunished.
And the Parisians were again quick to punish the visitors. They launched wave after wave of attacks and, although Edinburgh initially survived, it was only a matter of time until Racing broke through.
They won the ball from the top of a five-metre line-out and launched a powerful rolling maul that left Edinburgh in disarray before crashing over the try-line with Arous the beneficiary.
Edinburgh responded through the boot of Laidlaw, but they were dealt a blow when Brown was stretchered off after a heavy collision with Juan Pablo Orlandi.
Edinburgh refused to throw in the towel and continued to battle, but Maxime Machenaud put the result beyond doubt with a penalty with just minutes to spare.
Scorers – Racing Metro 92: Imhoff, Ben Arous tries; Barkley 2 pens, Machenaud pen. Edinburgh: Laidlaw 3 pens.
Racing Metro 92: Hernandez; Vakatawa, Bousses, Estebanez, Imhoff; Barkley, Descons (Machenaud 69); Brugnaut (Orlandi 56), Bianchin, Sa (Ben Arous 55); Metz ( 59), Van Der Merwe; Battut (Gerondeau 66), Cronje, Matadigo (Le Roux 53).
Edinburgh: Tonks; Brown (Jones 64), De Luca, Scott, T Visser; Laidlaw, Rees (Francis 54); Yapp (Jacobsen 64), Ford (Titterrell 65), Cross ( 42); Gilchrist, Cox (Parker 66); Denton, Grant, McInally.
Referee: P Fitzgibbon (Ireland).