The eagerly-awaited tie pitted Jurgen Klopp's successor against the man initially tipped to replace the German on Merseyside, Xabi Alonso, who masterminded Leverkusen's astonishing Bundesliga Invincibles run last season.
Liverpool battled their way to a goalless stalemate in the first half of Tuesday's game, having suffered a couple of scares as Leverkusen bombed forward, as Jeremie Frimpong had a goal disallowed on the stroke of the break.
However, the floodgates opened in the second half, where Colombian hotshot Luis Diaz came up with his first hat-trick in Liverpool colours, while Cody Gakpo also registered his first-ever goal in the Champions League proper.
By overseeing Liverpool's emphatic triumph over the German champions, Slot set a new record for the most games won in a manager's first 16 games at the helm of a Premier League team, earning 14 victories in his short time in charge.
Slot leaves Mourinho, Carlo Ancelotti in his wake
The Dutchman has now eclipsed the previous record holders, Jose Mourinho and Carlo Ancelotti, who each won 13 of their first 16 games in charge of Chelsea in 2004 and 2009 respectively.
As Slot celebrated another historic evening on Merseyside, former record holder Ancelotti saw his Real Madrid side suffer a shock 3-1 home loss to AC Milan, leaving the holders six points behind Liverpool in the 36-team Champions League table before their meeting at Anfield on November 27.
Since stepping into Klopp's shoes, Slot's only setbacks have been a 1-0 home defeat to Nottingham Forest and 2-2 draw away to Premier League title rivals Arsenal, having masterminded four wins from four in the Champions League so far.
No other team also boasts 12 points from 12 in the 2024-25 UCL campaign - Sporting Lisbon and Monaco are the Reds' closest challengers with 10 - although Aston Villa have the opportunity to draw level with them when they take on Club Brugge on Wednesday evening.
At the close of play on Tuesday, the Kop showed their appreciation for Slot by breaking out into song, although the Liverpool coach insisted that Alonso also deserved to have his name bellowed out just as much as him.
Slot pays tribute to Klopp, Alonso after "special" song
"It's always better for a manager that this happens than when they start to boo! It's special. It was special from the start and, therefore, I think I have to thank Jürgen [Klopp] because he was the one who came up with the song," Slot told reporters in his post-game press conference.
"It is always special if you are a player if they sing for you. Some players get used to this - I didn't, they only sung a few times for me in my playing career.
"That's what you see a bit more [and] people singing for a manager is not that common, at least not in Holland but maybe here it happens a lot.
"So, it was nice to hear today, but I also like it a lot that after that they sang for Xabi as well because he was so special for this club, so he deserves it for this, but also his achievements at Leverkusen - champions last year, won the cup, played a final in Europe. For all these reasons, he deserved the fans to sing for him as well."
Liverpool - who are also two points clear of Manchester City at the top of the Premier League table - now prepare to host Aston Villa on Saturday night before the November international break.