Lucien Favre's men were in control for much of the match, but it was a ruthless second-half display that did most of the damage, as they scored four times after the break to comprehensively defeat their relegation-threatened visitors.
Full-back Achraf Hakimi broke the deadlock with a fine strike, and while Hannover managed to tighten up at the back until half-time, Dortmund were rampant in the second half.
Reus – set up by Hakimi – got a deserved goal after an hour, before Mario Gotze and Raphael Guerreiro added to things, and, although Benjamin Hadzic at least got Hannover on the scoreboard, Axel Witsel rounded things off at the end.
After some earlier Reus chances went begging, the breakthrough arrived in the 24th minute – Hakimi sending a fierce strike into the right side of the net after a clever one-two with Guerreiro.
Something of a lull followed, but Dortmund exploded into life again in the second half.
Reus doubled the lead in sumptuous fashion with 60 minutes played, receiving Hakimi's cut back after he had robbed Miiko Albornoz and the Germany star produced a delicate first-time chip with the outside of his foot to beat the stranded Michael Esser.
Gotze then got in on the act, tucking home from a tight angle after a solo run and pass from Jadon Sancho, before Guerreiro netted in similar fashion 23 minutes from time following Reus' pass.
Hadzic deflected a shot in as Hannover pulled one back in fortuitous fashion towards the end, but it had no impact on the result, with Witsel finding the net from the edge of the box in stoppage time to put more pressure on defending champions Bayern Munich ahead of their clash with Stuttgart on Sunday.