Coach Joachim Low was absent again – having also missed the win over Belarus – due to an injury sustained in a "sporting accident" last month, but Estonia were so poor his unavailability was barely noticed in an emphatic win led by Reus and Gnabry.
The Borussia Dortmund star opened the scoring early on and also got Germany's spectacular fifth, with Gnabry, Leon Goretzka and Ilkay Gundogan netting in between.
After scoring five in the first half for the first time since thrashing Brazil 7-1 at the 2014 World Cup, it appeared to ease off a little in the second 45, though Gnabry got himself a second, before Timo Werner and Leroy Sane rounded things off.
Germany remains three points behind Group C leader Northern Ireland, who have played a game more.
Germany began with a swagger and carved Estonia open 10 minutes in, as Thilo Kehrer played a low first-time cross into the box from the right and Reus found the roof of the net.
Gnabry converted soon after with an easy close-range finish from Sane's squared pass, and Goretzka got in on the act with 20 minutes played, meeting Joshua Kimmich's lofted delivery with a glancing header into the bottom-left corner.
Joonas Tamm impeded Goretzka's off-the-ball run in the box a few moments later to concede a penalty, which Gundogan confidently dispatched.
And Reus made it 5-0 close to half-time – his gorgeous 30-yard free-kick finding the top-right corner.
After something of a lull, Germany resumed the battering and increased the deficit just past the hour, with Gnabry tapping in from Marcel Halstenburg's low delivery.
Werner – introduced for Reus in the 66th minute – beat the approaching Sergei Lepmets with a clever chip towards the end, and Sane rounded wrapped things up with a curling finish despite appearing to stray offside.