Mbappe put PSG ahead inside three minutes and Cavani grabbed his fourth goal in three Champions League outings before half-time.
Neymar scored a free-kick midway through the second period with his ninth goal for the club since his record-breaking move from Barcelona, before Angel Di Maria came off the bench to complete the rout.
Swiss prosecutors opened a corruption probe into PSG president Nasser al-Khelaifi last week over the sale of World Cup media rights, but the Qatari was in attendance in Belgium to watch his expensively-assembled side cruise to victory.
The French Ligue 1 leaders are now three points clear of Bayern Munich, who saw off Celtic 3-0 in Germany, at the top of Group B ahead of the home match against bottom side Anderlecht on October 31.
“In the first period it wasn’t perfect with the level of control of the match,” said PSG coach Unai Emery.
“We were sometimes surprised on the counter-attack, but in the second half we found a better balance.
“The match started very well with that goal in the third minute. But then, for a moment, we lost track. We know there will be no easy games this season.”
Spaniard Emery made four changes to the side that stumbled to a 2-1 Ligue 1 win at Dijon on Saturday, with Cavani and Marco Verratti returning to the starting line-up.
PSG scored eight goals in the opening two wins against Celtic and Bayern Munich, and they didn’t waste any time in breaking the deadlock on Wednesday.
Close-season signing Mbappe found space inside the area before drilling home his second Champions League goal for the club through goalkeeper Matz Sels’ legs from a tight angle.
Anderlecht, bottom of the group after a disappointing 3-0 home defeat by Celtic last time out, grew into the game though as midfielder Sven Kums shot wide.
Paris retained a serious threat going forward to keep their hosts honest, but Neymar and Cavani both missed half-chances.
The away side found a second goal shortly before the interval, with the feted attacking trio of Neymar, Mbappe and Cavani all involved.
World-record signing Neymar’s powerful strike from distance was well saved by Sels, but 18-year-old Mbappe headed the rebound back across goal for Cavani to nod in his 12th goal of the season.
Anderlecht were tidy in possession without ever getting in behind the PSG defence, and they were hit on the counter-attack again early in the second half, only for Cavani to rattle the crossbar.
The Uruguayan could have had a hatful of goals as he had two efforts disallowed for offside and also produced a tame chip into the legs of Sels with only the ‘keeper to beat before Mbappe blazed the loose ball over a gaping goal.
Neymar ensured that all three of PSG’s forwards scored for the second Champions League away match in a row, as the Brazilian rolled a clever free-kick under the wall and into the bottom corner from just outside the box.
Anderlecht went close to a consolation goal as Henry Onyekuru hit the woodwork, but Hein Vanhaezebrouck’s men remained pointless and goalless.
Argentinian Di Maria raced clear before dinking in to complete the scoring, as PSG reached the halfway stage of the group having scored 12 goals without reply.