The 25-year-old Czech striker took his season tally to 12 league goals after scoring all of his four goals in a remarkable second half performance, to stretch Leverkusen's unbeaten run to four consecutive league games and lift them to 27 points.
Seconds after a Fuerth effort that hit the back of the net was ruled offside Leverkusen went 2-0 up with Edmond Taposba's header in the 17th.
Fuerth, who have now lost a record-extending 12 league matches in a row, briefly revived their hopes in the 33rd when Jeremy Dudziak started a move and finished it with a low drive.
But goals either side of the break for Leverkusen killed off the game. Piero Hincapie drilled in their third in first half stoppage time before Schick turned from provider to scorer to net their fourth from close range in the 49th.
The forward then struck another three times in seven minutes, with Diaby, who terrorised the Fuerth defence with his runs down the wing, helping set up two of those goals.