Edinson Cavani and Kylian Mbappe were absent, although the latter was involved in a pre-match FIFA World Cup presentation at Parc des Princes, but Neymar helped ensure a comfortable victory for last season's unstoppable champion.
The Brazilian scored early, capitalising on a Brice Samba mistake to slot in a Christopher Nkunku pass, with Adrien Rabiot adding a second from Angel Di Maria's excellent assist before the break.
Gianluigi Buffon's Ligue 1 debut was mostly uneventful, the former Juventus and Italy goalkeeper able to keep a clean sheet after Stef Peeters hit the post with a free-kick, while Timothy Weah capitalised on another Samba error to complete the scoring in the 89th minute with his first Ligue 1 goal.
Neymar opened his 2018/2019 account inside 10 minutes, finishing off Nkunku's throughball after a disastrous pass out from goalkeeper Samba.
A second PSG goal inevitably arrived in the 35th minute, Di Maria dancing clear of the defence through the right channel to square a low cross that Rabiot couldn't miss from close range.
Buffon became PSG's oldest ever Ligue 1 player and the 40-year-old was surprisingly busy in the first half, beating away a powerful effort from Malik Tchokounte before reacting in mid-air to tip away a cross that deflected off team-mate Thiago Silva.
The goalkeeper was helpless as Caen went close to getting on the scoresheet in the 52nd minute, though, as a fine free-kick from Peeters bounced off the inside of Buffon's right-hand post.
Although Neymar appeared determined to add more goals after a disappointing FIFA World Cup in Russia with Brazil it was his replacement who added a late third.
Samba had tipped Weah's shot on to the post but then tried to do too much with a backpass, allowing the substitute to race in and knock the ball into the goal from close range to get Tuchel's men up and running.
Guingamp hosts PSG next weekend as Tuchel looks to continue a promising start to the new season, while Caen will hope for a better result in its first home game of the season against Patrick Vieira's Nice, which also lost this weekend.