The World Cup winner kicked three conversions and produced a commanding display as Racing ran-in five tries to move top of pool three.
Carter played 64 minutes on his debut before being substituted to a standing ovation at the Stade Yves-Du-Manoir.
Henry Chavancy, Eddy Ben Arous and Brice Dulin scored before half-time and the latter got a second after the interval to make sure of the bonus point for the Parisians.
Jim Mallinder admits he nearly replaced match-winner Stephen Myler
30/04/2016 AT 18:29
Juan Imhoff completed the rout with a fifth try shortly before the end as Racing sent out a stern warning to the rest of Europe.
The Glasgow Warriors also enjoyed a thumping win, beating the Scarlets 43-6.
[FULL MATCH REPORT: Six-try Warriors smash Scarlets in Champions Cup]
Stade Francais won in almost equally emphatic fashion away in Italy, crushing Benetton Treviso 50-17.
[FULL MATCH REPORT: Stade Francais stampede to victory over Treviso]
At Stade Olympique Yves-du-Manoir, Carter had created the space for Racing's first try with a lovely show-and-go and when the ball was recycled back, Joe Rokocoko was able to spin the ball out wide for Chavancy to go over in the corner.
It allowed Carter to get his first points in a Racing shirt with a superb conversion from out wide.
Racing almost got a second after quarter of an hour but Imhoff was hauled down by a superb last-ditch tackle from Tom Stephenson.
Ben Arous got Racing's second after 19 minutes after some strong carries by the home side's pack and he was not going to be stopped from five metres.
Carter added his second conversion and then nearly got on the scoresheet himself when his kick forward was fumbled by George North but the outside-half couldn't gather the loose ball.
A JJ Hanrahan penalty gave the visitors a brief foothold in the game but that disappeared when Dulin intercepted Victor Matfield's pass and raced 80 metres for Racing's third.
There was controversy a minute before half-time when Luther Burrell appeared to score for the visitors but referee George Clancy disallowed the try, despite not being able to communicate with the TMO.
Racing secured the bonus point three minutes after the break when Dulin got his second try after a devastating run from prop Ben Tameifuna.
There was frustration for the visitors with 20 minutes to go when Stephenson got over the line only for Clancy to call play back for a forward pass from replacement outside-half Stephen Myler.
Both sides then enjoyed periods of pressure in the final quarter but Racing saved their best for five minutes from the end when they produced a devastating counter-attack that finished with Rokocoko putting Imhoff over for their fifth try.
Teimana Harrison stars as Northampton bounce back to sink Bath
30/04/2016 AT 16:56
Teimana Harrison stars as Northampton bounce back to sink Bath
30/04/2016 AT 16:59