Barcola took a pass from Ousmane Dembélé after half an hour and steered a right-foot shot inside the far post.
Lee got his third goal of the season to double the home side's advantage 12 minutes into the second half and Barcola added his second with a simple tap in after 68 minutes.
Arnaud Kalimuendo scored a consolation goal for Rennes from the penalty spot.
Rennes had a second goal chalked off by VAR with two minutes to end any hopes of a comeback.
Barcola'd fifth and sixth goals of the season took him to the top of the Ligue 1 scoring charts, one clear of Marseille's Mason Greenwood.
PSG have 16 points from their first six games. Marseille are also unbeaten and have 13 points from five matches. The south coast club play at Strasbourg on Sunday.
Rennes are in eighth place with seven points from six games.
Auxerre beat Brest 3-0, also on Friday, to grab their second league win of the season and put the brakes on the visitors' recent run of form.
Brest were coming off two consecutive victories, including a 2-1 win over Sturm Graz in their first ever Champions League match.
But under the pouring rain in central France, Auxerre finally showed some of the form that won them promotion last year and staved off a fifth straight defeat in Ligue 1.
Elisha Owusu put the home side ahead with a left-foot shot after 26 minutes and captain Jubal doubled the lead from the penalty spot 11 minutes later.
Hamed Junior Traorè, on loan from Bournemouth, then got his second goal in two games 14 minutes into the second half.
The result leaves both teams with six points from six matches.
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