In the first of two meetings between the teams at the Parc des Princes either side of the international break, the difference was a series of mistakes by Lille at key moments.
The commotion off the field seemed to affect PSG's players as Nantes dealt the French champions a seventh Ligue 1 defeat of the season.
PSG's main focus is on extending the contracts of superstar forwards Kylian Mbappe and Neymar, both of whom will see their existing deals expire at the end of next season
Several media reports have suggested that an agreement with Neymar has already been reached.
Champions League: Paris Saint-Germain's Angel Di Maria to miss first leg of last-16 encounter against Barcelona
Di Maria suffered a thigh injury during the 2-0 Ligue 1 win against Marseille on Sunday and "he will not be at the Camp Nou" for the game on 16 February, Pochettino said.
Angel di Maria pounced on a misplaced pass to steer PSG ahead on 17 minutes at the Parc des Princes, with Pablo Sarabia heading in a cross from the Argentine to double the advantage.
The former Barcelona superstar's hat-trick in PSG's 5-1 win over the Turks when the game restarted a day later included two goals that were simply out of this world.
Ligue 1: Paris Saint-Germain working on contract negotiations with Neymar, Kylian Mbappe, says Leonardo
The deals of the attacking pair, who cost the French champions 402 million euros ($474 million) in two separate transfers, are up in 2022.
Di Maria struck in each half, with Moise Kean scoring the other, to move PSG up to 24 points, five ahead of second-placed Lille who take on Brest in Sunday's early fixture.
Di Maria's suspension meted out by Ligue 1's disciplinary commission was for spitting at Marseille defender Alvaro Gonzalez.
Ligue 1: Neymar in PSG squad for Marseille clash after beating COVID-19; Kylian Mbappé, Marquinhos still out
PSG coach Thomas Tuchel is not sure whether Neymar, winger Angel Di Maria, goalkeeper Keylor Navas or midfielder Leandro Paredes will start the game at Parc des Princes.
Mbappe, who took part in Monday evening's training session before learning the result of his test, is the seventh Paris Saint-Germain player to contract the virus. Neymar was among the first to test positive last week.
Ligue 1: PSG's Neymar, Angel Di Maria and Leandro Paredes test positive for COVID-19, according to reports
The 28-year-old Brazilian has COVID-19 as well as his Argentinian teammates Angel Di Maria and Leandro Paredes, the same anonymous sources said.
Champions League: Bayern Munich beat PSG by solitary Kingsley Coman goal to claim sixth European Cup
It was often a cagey final, with a bit of needle between the teams, but chances too, especially before Coman appeared at the back post to head in Joshua Kimmich's inviting 59th-minute cross and wrap up a treble for a team who had already won the Bundesliga and German Cup.
While most will be watching PSG forwards Neymar and Kylian Mbappé, or Bayern counterparts Thomas Müller and Robert Lewandowski, the title could come down to the likes of Ángel Di María and Serge Gnabry.
PSG became the first French league club to reach the Champions League final since Monaco in 2004, and they can become the second French team to win the title after Marseille in 1993.
Champions League: PSG coach Thomas Tuchel 'really surprised' to see video of players at party after Borussia Dortmund defeat
Neymar and Kylian Mbappe were among those attending a late party to celebrate the birthdays of Mauro Icardi, Edinson Cavani and Angel Di Maria
Ligue 1: League-leaders Paris Saint-Germain beat Nantes to move 15 points clear; Monaco scrape to first win under Robert Moreno
France striker Kylian Mbappe, who angrily snubbed Paris Saint-Germain coach Thomas Tuchel after being substituted in Saturday's 5-0 home win against Montpellier, set up the first goal in the 29th
Ligue 1: Kylian Mbappe bags brace as Paris Saint-Germain ease past Monaco; Rennes stake claim to Champions League qualification
The sides drew 3-3 in Paris on Sunday night in arguably the season's most entertaining game, although this time Paris Saint-Germain kept Monaco's attack quiet and exposed one of the worst defences in the league
Kylian Mbappe celebrated turning 21 with a silvery-looking haircut and two more clinical finishes as league leaders Paris Saint-Germain beat struggling Amiens 4-1