Visiting boss Xabi Alonso was offered a warm welcome ahead of kick-off, and proceedings only simmered after Danny Makkelie got the action started.
Victor Boniface and Cody Gakpo failed to work the respective goalkeepers with their early attempts, before Curtis Jones and Edmond Tapsoba gave them a routine save apiece.
Granit Xhaka and Trent Alexander-Arnold then hit what could have been more threatening strikes, although the considerable frames of Virgil van Dijk and Jonathan Tah were in position to block them.
Much of the first half went by without notable goalmouth action, but there was a flurry before the break. Díaz lured Xhaka into a foul on the edge of Die Werkself’s box, although Alexander-Arnold’s ensuing free-kick was deflected off-target by the wall.
Mohamed Salah and Gakpo then carved out promising openings before being denied by Lukas Hradecky.
Between those attempts, Jeremie Frimpong emphatically smashed the ball past Caoimhin Kelleher with a strike that proved inconsequential as the Dutchman had handled the ball in the build-up.
Leverkusen initially continued to make things difficult for their hosts after the restart, until Ryan Gravenberch glided through the crowd to tee up Salah, but an unconvincing swing of the Egyptian’s right boot saw the ball go harmlessly wide.
Diaz was far more clinical soon after, latching onto Jones’ perfectly-weighted pass and delicately flicking the ball over Hradecky.
After a 61-minute wait for Liverpool’s first goal, it took just two minutes for their second as Gakpo headed home from Salah’s cross having been kept onside by Piero Hincapie.
Diaz then added some extra gloss added to the scoreline for Liverpool in the closing stages.
The Colombian held off Jonas Hofmann to control Salah’s cross and finish and then capitalised on Hincapie’s block of Darwin Nunez's shot falling to him to complete his hat-trick as the Reds earned their 14th win from 16 matches under Arne Slot.
That includes a perfect record in the Champions League to take them top of the table for now, while Leverkusen are winless in their last two European matches.