Carter made a dream start to his career in French rugby at Racing 92 by helping the Parisian club to a bonus-point 33-3 victory over Northampton on Saturday to go top of European Cup Pool 3.
Carter kicked three penalties while letting half-back partner Mike Phillips dictate the pace of the game.
"We're really happy with that performance," said Phillips. "Dan's been great all week. He's obviously world class and will get better and better for us with each training session and each game. It's great for the squad. It was as if he's been here for a long time."
Also in the group, Glasgow gave themselves a lifeline while simultaneously all but eliminating Scarlets with a thumping 43-6 win over the Welsh outfit, who have lost all three games so far.
Australia international wing Taqele Naiyaravoro scored a hat-trick as the Scottish side plundered six tries to move to just three points behind Northampton.
Stade Francais went one better than Glasgow as they scored seven tries in a 50-17 rout away to Treviso in Pool 4.
Former New Zealand international centre Paul Williams scored two tries as the French champions led 50-0 before taking their foot off the gas and allowing Treviso to hit back with three tries of their own.
Also in Pool 4, Leicester took control of the pool with a 31-19 win at Munster.
Tries from Fiji wing Vereniki Goneva, New Zealand lock Mike Fitzgerald and England scrum-half Ben Youngs gave Leicester a 31-19 success that continues their perfect start to the group.
In Pool 2, Exeter stunned last year's runners-up Clermont 31-14 and even secured a bonus point thanks to Australian forward Mitch Lees's last minute try.
Clermont led 14-3 after 20 minutes but two converted tries from the England No.8 Thomas Waldrom put Exeter 17-14 ahead early after the break.
Zimbabwe-born flanker Don Armand stretched that lead with the third try seven minutes from time before Lees's bonus-point clincher at the death.
Exeter are level on 10 points at the top of Pool 2 with Ospreys, who beat Bordeaux-Begles 19-16.