Marquinhos opened the scoring for PSG - crowned champions of the top flight in midweek - in the 41st minute, shortly after Marvin Martin had been dismissed for a dangerous challenge on Yohan Cabaye.
France international Cabaye had to be stretchered from the field under the closed roof of Stade Pierre-Mauroy, casting doubt over his involvement in the FIFA World Cup, with coach Didier Deschamps set to name his preliminary squad next week.
Lucas Moura put PSG two goals up in the 65th minute, before substitute Blaise Matuidi grabbed his fifth league goal of the season late on.
The league’s previous record for a single season was 84 points – set by Lyon in 2005-06 – and PSG now stand two points clear of that marker with a match still to play.
Jonathan Delaplace grabbed a stoppage-time goal for Lille, whose bid for UEFA Champions League football will now go down to the wire after fourth-placed Saint-Etienne cruised to a 3-1 win at Nantes to close the gap between the sides to two points.
Zlatan Ibrahimovic returned from injury to make his first start in more than a month, but there was no place for Edinson Cavani in the squad amid reports the Uruguay international is unhappy at the Parc des Princes.
And it was Ibrahimovic who had the first opportunity to break the deadlock – his drive from close range bouncing over the crossbar via the leg of defender Simon Kjaer.
Franck Beria went down in the penalty area under the challenge of Lucas Digne in the 13th minute, but referee Ruddy Buquet waved away Lille's protests, as well as PSG's counter-claims the defender had gone down too easily.
Nolan Roux sent an effort wide of the right-hand post off the leg of Zoumana Camara midway through the half, although neither goalkeeper was being made to work too hard as the defences held firm.
Enyeama made a spectacular diving save from Cabaye shortly after the half-hour mark, but the former Lille man was writhing around on the turf moments later after a reckless challenge from Martin.
Having initially booked Martin, Buquet appeared to change his mind and soon had the red card held aloft.
PSG almost instantly took advantage of the extra man as Marquinhos leapt brilliantly to head home after Enyeama had palmed away Lucas' original effort.
Idrissa Gueye scooped over as Lille looked to pull level early on in the second period, before Marko Basa spurned two good opportunities.
And Lucas ended Lille's challenge when he slid the ball past Enyeama before setting up Matuidi with a fine through-ball, allowing the Frenchman seal PSG's record in style and securing a 26th league win of the season - equalling another Ligue 1 milestone.
Substitute Delaplace's strike at the death proved scant consolation, as Lille continue to sweat over their involvement in Europe's elite club competition next season.
