Marco Verratti curled in a terrific opening goal - his first in Europe since September 2014 - on the halfhour at the Parc des Princes, with Brazilian superstar Neymar firing in a second before the break.
The world’s most expensive player was involved in PSG’s third goal as well, as his free-kick was tipped onto the post with France international Kurzawa forcing in the rebound.
The left-back then headed in another from a Dani Alves cross and completed an improbable treble with an angled drive as PSG increased its goals haul to 17 - with none conceded - in four Group B matches.
The French giant tops its section with a maximum 12 points, with Bundesliga leader Bayern progressing alongside it following a 2-1 victory away to Celtic.
Kingsley Coman pounced on hesitant Celtic defending to latch onto a long clearance upfield from goalkeeper Sven Ulreich and round Craig Gordon to slot into an empty net on 22 minutes.
Callum McGregor slotted in a second-half equaliser, but Javi Martinez’s brave towering header - which left the Spaniard bloodied - clinched qualification for the Germans in Glasgow.
Jose Mourinho’s Manchester United was made to wait to seal its passage into the next round despite a 2-0 win over Benfica.
Benfica’s Mile Svilar, who became the youngest goalkeeper in Champions League history a fortnight ago, suffered more misfortune at Old Trafford as his own goal handed United a 45th-minute lead.
The 18-year-old, at fault for the 1-0 defeat in Lisbon, atoned for that error by saving an Anthony Martial penalty, but Svilar was helpless when Nemanja Matic’s low drive cannoned off the post before hitting him on the arm and squirming over the line.
Daley Blind wrapped up victory from the penalty spot on 78 minutes after a foul on Marcus Rashford.
Chelsea squandered a chance to secure a berth in the knockout stages as Stephan El Shaaraway inspired Roma to a 3-0 success over the Premier League champion in Italy.
El Shaarawy drilled Roma ahead after just 40 seconds at the Stadio Olimpico as he ran onto an Edin Dzeko knockdown to slam home from the edge of the area.
The Italy striker netted a second on 36 minutes with Diego Perotti rifling in a third from 25 yards as Roma replaced Chelsea at the top of Group C with two matches remaining.
Roma is on eight points, one above Chelsea, but Atletico Madrid is heading for elimination following a 1-1 draw at home to Qarabag.