The Georgia winger collected the ball just outside the penalty area and dribbled past three players before passing to Ousmane Dembélé, whose slightly deflected shot flew past goalkeeper Yehvann Diouf in the 47th minute.
Kvaratskhelia joined from Napoli last week in a deal worth $A116 million and was paraded before fans at Parc des Princes before Saturday's game, holding up the No. 7 jersey in the driving rain.
Reims usually cause PSG problems and did so again when Japan winger Keito Nakamura finished off a smart team move in the 56th.
Defending champions PSG remain unbeaten in Ligue 1 but have drawn five of 19 games and second-placed Marseille can move within seven points with a victory at fifth-placed Nice on Sunday.
Earlier, Maghnes Akliouche scored a spectacular goal and set up an easy one as Monaco beat Rennes 3-2 to move up to third place.
Akliouche put the home side ahead in the 16th minute with a brilliant overheard kick from Vanderson's cross. But right back Mahamadou Nagida equalised just before the break.
Shortly after Mika Biereth scored his first goal for Monaco in the 52nd, latching onto a pass from Lamine Camara and slotting through the legs of the goalkeeper, Akliouche's pass gave Aleksandr Golovin an open goal for 3-1.
Amine Gouiri pulled a goal back for struggling Rennes, starting and finishing the move.
Lille needed to win at Strasbourg to reclaim third spot from Monaco, but lost 2-1 despite taking an early lead through Moroccan striker Osame Sahraoui.
Brazilian midfielder Andrey Santos equalised in the 70th with a powerful strike from outside the penalty box and Dutch striker Emmanuel Emegha headed home four minutes later for Strasbourg, who climbed into eighth.
Coach Bruno Genesio's had been unbeaten in Ligue 1 since losing at Saint-Etienne on September 13.
But Nice can take Lille's place in fourth by beating Marseille.
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