Laurent Blanc's side fell behind to an early Alejandro Bedoya goal at the Parc des Princes, but Ibrahimovic took his league tally to eight for the season with two well-taken strikes.
Ibrahimovic's first came from a Lucas Moura cross after 34 minutes, the 33-year-old getting in front of his marker to tap past Remy Riou.
A stunning free-kick gave Ibrahimovic a second goal in the opening minutes of the second half and PSG promptly coasted to victory.
PSG's advantage could have been greater had Lucas and Ezequiel Lavezzi not wasted good opportunities, but it mattered little as Blanc's side prepared for their midweek UEFA Champions League showdown with Barcelona with a comfortable win.
Victory moves PSG to the top of the table at the expense of Marseille, who play on Sunday, while Nantes are eighth.
Blanc opted to rest six players ahead of their trip to Camp Nou on Wednesday, but there were recalls for Ibrahimovic and Marco Verratti.
Bedoya was one of three changes for the visitors and he had an immediate impact with the game's opening goal after eight minutes.
A surging run from midfield was halted by a strong Thiago Silva challenge, but the loose ball dropped perfectly for Bedoya and the American fired beyond Salvatore Sirigu into the top corner.
Nantes were unlucky not to have a second four minutes later when Verratti cynically brought down Georges-Kevin N'Koudou and, from the resulting free-kick, Oswaldo Vizcarrondo volleyed home at the back post, but his effort was ruled out for offside.
That let-off seemed to ignite PSG and chances quickly began to materialise, but Serge Aurier and Lucas were unable to find the final ball.
However, the hosts got their goal after 34 minutes as Ibrahimovic got in front of Vizcarrondo to poke Lucas' low cross under Riou.
PSG should have gone into the break ahead, but Riou came to Nantes' rescue in the final minute, the goalkeeper reacting well to save Silva's header with his knees.
The home side did not have to wait long for that second goal, though, as Ibrahimovic thundered a 20-yard free-kick past Riou two minutes after the break.
The Sweden international fired the ball over the wall and into the top corner after Olivier Veigneau had fouled Verratti.
Having taken the lead, PSG assumed control of proceedings and Lucas should have extended their advantage two minutes after the hour.
Ibrahimovic rose above his marker and played a cushioned header into the Brazilian's path, but he dragged his shot wide of goal without testing Riou.
Another chance went begging seven minutes later as Aurier made excellent ground down the right and his low cross was met by Lavezzi, but he was unable to guide the ball into the far corner, his effort just curling wide.
Sirigu, who had been untroubled for the entire second half, was eventually called into action after 76 minutes as a swift counterattack saw substitute Lucas Deaux fire towards goal, but the Italian was more than equal to his tame effort.
Blanc was able to give Verratti, Lucas and Javier Pastore a rest in the second half with the hosts in control, ensuring the French champions are at full strength for their trip to Spain.
