Nagelsmann, whose sacking in March 2023 led to Tuchel's arrival, was tipped to return to Bayern, but has now extended his contract with Germany until 2026
The Brazil striker fired home with a superb free kick after Yuri Berchiche had opened the scoring on the stroke of halftime, with Giovani Lo Celso sealing a straightforward victory in the closing stages.
The win put PSG on 62 points from 24 games with second-placed Olympique de Marseille, who hammered Metz 6-3 away on Friday, on 51.
Lille are 17th on 25 points, one point above safety.
PSG went ahead in the 45th minute when Berchiche netted with a low shot after the Lille defence had failed to clear Edinson Cavani's cross.
Neymar, who was doubtful after taking a knock earlier this week, doubled the tally with a 17-metre free kick into the top corner.
Lo Celso then scored his first Ligue 1 goal with a fine lob over Mike Maignan in the 87th.