Man Utd still have work to do in order to book their place in the last-16 after FC Basel bagged a late winner in Switzerland.
PSG set a new Champions League group stage goalscoring record (24) after trouncing sorry Celtic 4-1.
Elsewhere, Atletico Madrid kept their qualification hopes alive with a 2-0 win over Roma, Juventus and Barcelona played out a goalless draw, Sporting Lisbon beat Olympiakos 3-1, and Bayern Munich came away from Anderlecht with a 2-1 win.
Earlier in the evening Chelsea hammered Qarabag 4-0, and CSKA Moscow beat Benfica 2-0.
They've taken their time in the second-half but at last PSG bag their fifth goal (5-1) of the night, which in turn means the French giants have broken the Champions League group stage goalscoring record with 22 goals...and they're not finished yet...
...as they instantly grab another to make it 6-1...then another to make it 7-1!
The goals came courtesy of Verratti, then Cavani who is now on a hat-trick, followed by a pearler from Alves.
It's a must win clash for Atletico Madrid at home to Roma and they've just stormed ahead in the 69th minute thanks to an absolute stunner from star man Griezmann.
The ball is whipped into the mixer to the Frenchman who acrobatically volleys the ball into the back of the net.
What. A. Hit.
Not much to report on across the board in the second-half, except that Anderlecht have just bagged a deserved equaliser at home to German giants Bayern Munich.
The goal came from Hanni who cancelled out Lewandowski's 51st minute opener.
Man Utd's clash with Basel remains goalless, while Celtic are still 4-1 down to PSG.
The half-time whistles go in the six Champions League matches, four of which remain goalless, including Man Utd's clash with Basel in Switzerland.
Over in Paris, Celtic took a shock lead in the first minute, however PSG are now running riot, leading 4-1 at the break.
The only other game with goals is Sporting Lisbon vs Olympiakos, with the home side 2-0 up after 45 minutes.
1 minute in and Celtic are in dreamland after taking a shock lead...fast-forward to the 35th minute and they're 4-1 down...
At the rate this is going it could be a cricket score.
This time the unmarked Mbappe gets in on the act, smashing home from the right side.
It's all too easy for PSG, who need one more goal to break the Champions League group stage goalscoring record.
It's a blink and you'll miss it series of quick-fire passes from PSG who surge ahead through...yep you guessed it, that man Neymar.
PSG look so good on the ball, and the crisp collection of passes bamboozle the Celtic backline, with Neymar finishing off the well-worked move.
Celtic's shock lead lasted all of eight minutes.
PSG make a lightning break following a sloppy pass from Scott Brown in the middle of the park.
Cavani storms forward, before finding Neymar on the left. The Brazilian ventures into the penalty area and shoots across goal past Gordon, who perhaps should have done better there.
We are off in the six Champions League fixtures, which feature two British teams in Man Utd who face FC Basel, and Celtic who clash with PSG in Paris.
Elsewhere, picks of the rest include Juventus' battle with Barcelona, and Atletico Madrid's must-win game at home to Roma
Chelsea are through to the knockout stages of the Champions League after registering a comfortable 4-0 win away to Qarabag.
The Blues are the third English club to progress, joining Tottenham and Man City in the pot for the last-16.
Goals from Willian (2), Hazard and Fabregas helped Antonio Conte's men cruise through against a side that played the majority of the match with 10 men.
Willian picks the ball up on the edge of the area, shifts the ball onto his right foot and fires low and hard into the bottom right corner.
Chelsea are now 4-0 up and the Brazilian is on a hat-trick...
Chelsea are in cruise mode.
The visitors win a penalty, which is coolly stroked into the left corner by Fabregas...but no, the referee orders a retake, which the Spaniard fires into the bottom left corner to make it 3-0.
Moments earlier Rudiger slots the ball through to the unmarked Morata who, in a great position, drags his shot wide of the post.
Then, just after Morata finds the back of the net but the goal is ruled out for offside.
We are back under way in the early Champions League kick-off between Qarabag and Chelsea.
Chelsea went into half-time cruising thanks to goals from Hazard (penalty) and Willian, with their opponents down to 10 men.
The Blues are strolling through to the last-16, and will no doubt enhance their tally in the second-half.