PSG maintained their nine-point lead at the top of Ligue 1 with a 1-0 win over the relegation-threatened club, a second-half strike from Javier Pastore enough to earn all three points for Carlo Ancelotti's men.
However, the French capital outfit finished the game with nine men as Marco Verratti and then Beckham saw red in a fiery contest.
Beckham's dismissal looked to be especially harsh, the 37-year-old was shown a straight red for a foul on Youssef Adnane, but replays showed the former England international made no contact with the Evian striker.
The controversy led to ugly scenes at the end, with Evian's Saber Khelifa and PSG goalkeeper Salvatore Sirigu both dismissed in a post-match melee sparked when Blaise Matuidi appeared to celebrate in front of the home side's dugout.
Leonardo suggested that referee Olivier Thual was at fault for the manner in which the game concluded.
"It was tense match, but there's no need to go over the top. The referee lost his cool," he said.
"The referee lacked lucidity. He made mistakes. The red card shown to Beckham, for example, was really unfair."
PSG can now win the league title for the first time since 1994 if they beat Valenciennes and Marseille fail to overcome Bastia. 
Ancelotti was left satisfied by the performance against Evian, and is hopeful his players can now finish the job.
"The game was well played. We did not begin with a lot of intensity but, after 20 minutes, we controlled the game," the Italian explained.
"We scored a fantastic goal, with a lot of movement. We needed a second one, and [not getting one meant] Evian gained in confidence as they hoped to equalise. 
"After the red cards for Verratti and Beckham, we lost a little control.
"Nine points ahead, the title is very close. With a victory at home on Sunday, we will win it. It would be a great opportunity to have a party with our fans."