The Gabon international didn't take long to double his tally for the evening, again converting from close range following Lukasz Piszczek's cross.
The striker nearly capped a memorable first half with his third, but this time he rattled the woodwork after good work from Henrikh Mkhitaryan.
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Reus then extended the lead further with an effort from all of 25 yards to put the German side firmly in control at the interval.
The German side wasted two good chances in quick succession towards the hour mark through Reus, with the second attempt saved by Fernando Muslera after the initial effort had sailed over the crossbar.
Jurgen Klopp's side were in cruise control in the second period and their flowing football should have been finished off by Shinji Kagawa on 66 minutes but the Japan international dragged his shot wide.
Substitute Adrian Ramos put the gloss on the result with seven minutes of normal time remaining moments after coming on in place of the injured Kagawa.