Javier Pastore scored the only goal five minutes into the second half to put leaders PSG on 73 points, nine ahead of second-placed Olympique Marseille with four matches left.
Beckham, who came on as a second-half substitute, was shown a straight red for a foul on Youssef Adnane two minutes into stoppage time after Marco Verratti had been sent off in the 80th when he picked up a second yellow card.
A mass brawl erupted after the final whistle and Evian's Saber Khlifa was shown a red card by referee Olivier Thual, who also asked for PSG goalkeeper Salvatore Sirigu to join him back on the pitch.
In a surreal scene, Sirigu was walking back towards the field but made a U-turn after being ordered to by a PSG representative.
It was not clear whether Sirigu was handed a red card.
"This kind of thing happens in a football game, tempers flared a little bit, that's all," PSG defender Christophe Jallet told French television Canal Plus.
PSG will be crowned champions for the first time since 1994 next Sunday if they get more points against Valenciennes at home than OM pick up against Bastia at the Stade Velodrome.
Olympique Lyon stayed third on 60 points after Yoann Gourcuff's second-half strike salvaged a 1-1 home draw against arch rivals Saint-Etienne earlier on Sunday.
Relegation-threatened Evian, who eliminated PSG from the French Cup quarter-finals last week, were not that lucky this time.
Zlatan Ibrahimovic's fierce 25-metre shot was saved by Bertrand Laquait as PSG got off to a good start.
Evian had their first chance in the eighth minute when Khlifa's dipping shot from the edge of the box went just over Sirigu's crossbar.
Laquait was then at it again to deny Ibrahimovic's soft volley from Maxwell's free-kick.
PSG's Ezequiel Lavezzi later showed another example of his clumsiness by fluffing a shot after collecting a brilliant pass from Ibrahimovic.
However, the breakthrough came when Pastore curled a shot from just inside the box past Laquait to put PSG ahead in the 50th minute.
Ibrahimovic and Lavezzi each missed a sitter shortly after the hour as PSG looked close to doubling their tally.
HIGH FOOT
The Sweden striker, in front of an open goal after Verratti's shot had bounced off the bar and into his path, skied his attempt over the bar while his Argentine team mate inexplicably failed to find the net after dribbling past Laquait.
Sirigu then pulled off a brilliant save to deny Khlifa's powerful shot and PSG remained under pressure, especially after Verratti was sent off.
The Italian midfielder was shown a second yellow card when he argued with the referee and was yelled at by coach Carlo Ancelotti as he passed by on his way back to the dressing room.
Beckham did not receive the same treatment after he was given his marching orders. The former England captain seemed
