Having started 2011 with a ten-point lead, Dortmund hit second-half goals in quick succession from teenager Mario Götze and two from 22-year-old Kevin Grosskreutz to seal the win.
With such a commanding cushion at the top of the liga, Dortmund can start dreaming of their first German title since 2002.
"I have been going to watch Dortmund since 1994 and I know what it's like to win the league title as a fan on the terraces," said Grosskreutz.
"I have been dreaming of this since I was a little boy and I'd love to hold the cup in my hands."
Although Leverkusen rallied in the game's final 15 minutes, Dortmund coach Jurgen Klopp, who has been tipped as a future manager of English giants Liverpool, was clearly delighted with his side's convincing away win.
"The plan was to continue to play our own style of football, which we did," said Klopp.
"The first goal settled the nerves and we weren't comfortable until we got the third goal."
Dortmund's clinical second-half performance overshadowed the eagerly anticipated return of Germany captain Michael Ballack from the leg injury which has kept him out of football since September.
Leverkusen coach Jupp Heynckes opted to delay the veteran's return by keeping him on the bench for the entire game.
Grosskreutz, who is tipped as a future Germany star, opened the scoring when he latched onto a handball by Leverkusen defender Daniel Schwaab and tapped his shot past Leverkusen's Germany goalkeeper Rene Adler on 49 minutes.
Just four minutes later, the attacking midfielder curled his shot around Adler after Dortmund goalkeeper Roman Weidenfeller's goal kick was headed on by striker Robert Lewandowski for Grosskreutz to blast home.
And Leverkusen's misery was complete when Grosskreutz turned provider as Götze beat Adler for the third time from close-range on 55 minutes.
Only a superb save from Adler stopped it from being 4-0 when substitute Lucas Barrios fired in a shot from the left flank from long-range which prompted a full-stretch save from the national goalie.
With 10 minutes remaining, Leverkusen striker Steffan Kiessling pulled a goal back for the hosts when he latched onto a cross from Renato Augusto to stab the ball into the net, injuring himself on the goalpost in the process.
The result sees Leverkusen drop down to third, while defending champions Bayern Munich open their 2011 campaign with a 17-point deficit to make up when they face Wolfsburg away on Saturday.