Up next for Dortmund is the first leg of their round of 32 Europa League tie against Atalanta on Thursday.
The hosts got off to a flying start when Robert Lewandowski scored for the 11th successive home game, in the sixth minute.
Franco Di Santo stunned the Allianz Arena by equalising in the 29th minute, burying his shot after Leon Goretzka mis-kicked from Breel Embolo's cross.
Reus was named Dortmund captain on his return after a cruciate ligament injury sustained last May in the German Cup final.
Dortmund lived dangerously with Hamburg threatening an equalizer, but substitute Mario Goetze sealed the win in injury time after Andre Schuerrle played him in to lift the ball over the onrushing goalkeeper.
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Officer Morelli was recognized in 2012 as the Westerville Division of Police Officer of the Year. The officers responded after police received a 911 call and the caller hung up.
After a great incisive pass from Reus, Christian Pulisic squared the ball across the face of the goal and it was Batshuayi who slid the ball into the back of the net - and afterwards celebrated in a very similar acrobatic fashion to that of a certain Pierre-Emerick Aubameyang.
Runaway leader Bayern Munich was hosting Schalke later.
Valentino Lazaro fired Hertha ahead before the break on a counterattack, when Vladimir Darida played the ball through.
Hamburg, the only ever-present team in the Bundesliga's 55-year history, are 17th in the 18-club table with 17 points, three adrift of Mainz 05 in the relegation playoff spot. Hamburg defended well and looked more like scoring.
Hannover ended Freiburg's nine-game unbeaten run with a 2-1 win at home to consolidate its midtable spot, level on points with Hoffenheim and Augsburg.