Sidney Sam struck twice and Stefan Kiessling and Eren Derdiyok were also on target while former Chelsea player Michael Ballack looked sharp.
"I am very satisfied with Michael but I don't yet know whether he will start against Chelsea. We will not reveal our lineup today," coach Robin Dutt told reporters.
"Augsburg kept us very busy so it is important to recover quickly from this match."
Leverkusen, who meet the Londoners in Champions League Group E on Tuesday, now have 10 points from five Bundesliga matches.
With Ballack partnering Simon Rolfes in midfield for the first time this season, the game got off to a frantic start.
The hosts took a fifth-minute lead through Japanese Hajime Hosogai but last year's Bundesliga runners-up Leverkusen levelled seconds later thanks to Sam.
Augsburg, looking for their maiden Bundesliga win, twice went close before the visitors struck again when Germany forward Kiessling was left completely unmarked in the 23rd minute and slotted the ball in from 10 metres.
Leverkusen were then lucky not to have Daniel Schwaab sent off when he brought down the charging Sascha Moelders just outside the box.
Sam sealed their win with a clever left-foot shot against the run of play on 72 minutes before substitute Derdiyok completed the rout.
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