This lead was doubled less than 10 minutes later when Reus linked with teammates well before squaring to Klose, who again made no mistake to net his 67th international goal, a tally that puts him one behind the legendary Gerd Muller as Germany's top scorer.
Mesut Ozil and Reus both squandered good chances in the space of a minute, but just seconds later the home side were three up. The ball was swung into the Sweden box, allowing Thomas Muller to nod it down to Per Mertesacker, who fired past Andreas Isaksson.
Germany extended their lead even further 10 minutes into the second half when Muller once again provided an assist, this time for Ozil who fired the ball across Isaksson and into the corner.
The fourth goal seemed to galvanise Sweden, however, and they restored a measure of hope with two goals in quick succession. First, Zlatan Ibrahimovic nodded home to make it 4-1 before Mikael Lustig squeezed his shot past Manuel Neuer.