Real Madrid midfielder Kroos curled in a shot after a free-kick routine with Marcos Reus on the edge of the box. It completed a comeback from 1-0 down for the holders, who were on the brink of elimination from Group F after Ola Toivonen put Sweden in front on 32 minutes.
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Reus equalised three minutes after the break, but Die Mannschaft still looked doomed when centre-back Jerome Boateng was shown a second yellow card and sent off eight minutes from time.
Had Germany not overcome the deficit, it would've marked the first time they lost their opening two games at a World Cup. The goal also means the defending champions, beaten by Mexico last time out, need to beat already-eliminated South Korea to qualify for the last 16, provided Sweden don't better their result against the Group F leaders.
El Tri still aren't sure of progress after Kroos' late strike, so they have all the motivation they need to get a positive result against crestfallen Sweden. Kroos' goal could be the turning point for a Germany squad embroiled in apparent turmoil before the 95th minute at Sochi's Fisht Stadium.