Kolisi, 32, joined the side after lifting a second Webb Ellis trophy late last month but will make his debut for the Parisians next Sunday against La Rochelle.
The iconic Springbok followed the game alongside Chelsea captain Reece James, as the footballer benefitted from his free time during the international break to take in the match.
Racing's victory in rainy conditions moves them above Stade Francais to top of the table based on their head-to-head record.
"I've been involved in many big derbies internationally with England-Wales, England-France, or club level with Leinster-Munster, and it's right up there the feeling in the changing room," said Racing coach Stuart Lancaster.
"It wasn't perfect, but I felt all the big players stood up and played and we deserved it in the end," the former England and Leinster boss added.
Kolisi's new outfit led 10-6 at the break thanks to centre Henry Chavancy's try and four points from the boot of South African fly-half Tristan Tedder.
Stade Francais fly-half Joris Segonds made it a one-point game just after the interval with his third penalty of the match.
Racing, champions in 2016, held on for victory, an eighth straight at their rivals' Stade Jean-Bouin, as promising French scrum-half Nolann Le Garrec kicked a 54th-minute penalty.
Later, Test rugby's most capped player in former Wales and British and Irish Lions captain Alun Wyn Jones makes the final appearance of his career as Toulon head to Clermont.
Third-placed Pau, the surprise package this season, can leapfrog Stade Francais and Racing to top spot if they beat Bayonne.
France captain Antoine Dupont unusually starts at fly-half as Toulouse head to Castres, days after it was announced the playmaker would miss a big chunk of the 15-a-side season to prepare to play sevens at next summer's Paris Olympic Games.
On Sunday, Bordeaux-Begles travel to double Champions Cup winners La Rochelle, who have tasted victory just twice this campaign.
