The Brazilian, who signed for a world record £198m from Barcelona, scored the third goal in PSG's 3-0 win over Guingamp on Sunday.
Neymar helped carve out the first real chance in the 15th minute, combining neatly with Thiago Motta to free Cavani but Johnsson saved with his legs to deny the Uruguayan.
And, with eight minutes remaining the PSG fans were treated to what they had been dreaming of as Neymar got his name up in lights, Cavani unselfishly squaring the ball back for the Brazilian to tap home his first goal for the French giants.
In the 35th minute, he scooped a delicate cross above the defence, but Marquinhos's header crashed on to the bar.
Starting on the left of a front three also featuring Cavani and Angel Di Maria, but given considerable licence to roam, the 25-year-old produced plenty of impressive moments in what will surely go down as a memorable start to his PSG career.
Neymar celebrates with Cavani. Cavani usually would have gone alone from there.
With Unai Emery's side already leading 1-0 thanks to Jordan Ikoko's freakish own goal, Neymar assisted Edinson Cavani with a wonderful pass before the roles were reversed eight minutes from time for the Brazilian to tap home.
Falcao scored twice before the break and once after to take his tally to four goals in two games, while Jemerson netted another.