Jeremie Frimpong's 43rd-minute goal was ruled out for handball, but the visitors would fall behind when Curtis Jones' through ball found Luis Diaz, who scored an exceptional chip from close range in the 61st minute.
The Reds doubled their lead just a few minutes later when they countered from their own half and charged down the right side of Leverkusen's defence, before Mohamed Salah crossed towards an unmarked Cody Gakpo, who headed the ball into the net at the back post.
Diaz scored the third goal of the game after the ball to the back post from the right of the box by Salah, who notched his second assist of the match when Diaz collected the ball in the six-yard box and struck home.
The Colombian found time score his third and take home the match ball when the Reds countered through Darwin Nunez, who carried the ball into the penalty area but his shot rebound to Diaz, who could hardly miss from just yards out.
The result means that Liverpool now have 12 points from their four Champions League fixtures, and ended Tuesday in first place in the Champions League table.
Meanwhile, Leverkusen end the night on 7 points and are now in 10th place and occupy a round of 16 playoff spot.
Jones played a delightful pass to Diaz for his side's first of the game, sliding the winger-turned-striker through on goal past Edmond Tapsoba, before the Colombian dinked the ball into the net.
Anfield erupted again when Gakpo headed home from close range following a swift Liverpool counter-attack, but the Dutchman had an anxious wait as his goal was ruled out for offside before the decision was overturned by VAR.
Diaz grabbed his second of the game in the 83rd minute thanks to Salah's inch-perfect delivery into the box from the right, and the Colombian netted his third in the 92nd minute after Nunez's shot struck a Leverkusen defender and bounced into his path inside the penalty area.
LIVERPOOL VS. BAYER LEVERKUSEN HIGHLIGHTS
Luis Diaz goal vs. Bayer Leverkusen (61st min, Liverpool 1-0 Bayer Leverkusen)
Curtis Jones picks up the ball in a central area in Leverkusen's half and threads a fantastic through ball to Luis Diaz, who scoops the ball over a helpless Lukas Hradecky!
Cody Gakpo goal vs. Bayer Leverkusen (63rd min, Liverpool 2-0 Bayer Leverkusen)
Liverpool counter from their own half and work the ball to Salah on the right side of Leverkusen's defence, before the Egyptian plays a cross to an unmarked Cody Gakpo at the back post to make it 2-0 thanks to a VAR intervention that shows the Dutchman was onside!
Luis Diaz goal vs. Bayer Leverkusen (83rd min, Liverpool 3-0 Bayer Leverkusen)
Salah picks up the ball on the right of Leverkusen's defence again, and again he picks out a Liverpool forward in the box with a sublime cross, and this time Diaz controls the ball in the six-yard box before he strikes from close range for his second of the game!
Luis Diaz goal vs. Bayer Leverkusen (92nd min, Liverpool 4-0 Bayer Leverkusen)
Liverpool counter-attack once again and the ball is with Darwin Nunez inside the box, and his shot is blocked but the ball falls into the path of an unmarked Diaz, who makes sure not to miss!
MAN OF THE MATCH - LUIS DIAZ
Slot made two changes to the team that started against Brighton & Hove Albion last weekend, with Curtis Jones and Luis Diaz coming in for Dominik Szoboszlai and Darwin Nunez, and it is fair to say that that both repaid his manager's faith.
However, after scoring a hat-trick it is simply impossible not to give the man of the match award to the Colombian, who showcased his poacher's instincts inside the box for all three goals.
Diaz has often been criticised for his ball striking and impact in the final third, but the Colombian can be proud of his performance and has given Slot a selection dilemma for Liverpool's next game.
LIVERPOOL VS. BAYER LEVERKUSEN MATCH STATS
Possession: Liverpool 47%-53% Bayer Leverkusen
Shots: Liverpool 22-12 Bayer Leverkusen
Shots on target: Liverpool 8-4 Bayer Leverkusen
Corners: Liverpool 1-3 Bayer Leverkusen
Fouls: Liverpool 15-10 Bayer Leverkusen
BEST STATS
WHAT NEXT?
Liverpool return to Premier League action on Saturday when they host Aston Villa at Anfield, before taking on Southampton on November 24 after the upcoming international break.
As for Bayer Leverkusen, they travel to face VfL Bochum on Saturday in the Bundesliga, ahead of playing Heidenheim at Bay Arena on November 23.