Timo Werner said he was almost in tears after Toni Kroos' 95th-minute winner rescued German hopes of qualifying for the World Cup last 16.
Defending champions Germany were facing elimination when Sweden took a shock lead in the Group F blockbuster in Sochi until Marco Reus equalised and Kroos curled a stunning free-kick into the top corner for a dramatic 2-1 victory.
Germany – who had Jerome Boateng sent off late in the game for a second yellow card – are now level on three points with Sweden and three adrift of Mexico heading into Wednesday's clash with South Korea.
Indeed, Germany were beaten by Mexico in their opening encounter, while Carlos Vela and Javier Hernandez scored in the group leaders' win over the Koreans on Saturday.
Speaking afterwards, Germany forward Werner told reporters: "In the locker room it was pure joy.
"Some could hardly say anything. I almost had tears in my eyes on the pitch, because it was so cool. We deserve this. That could have been the turning point.
"After trailing 1-0, we were facing elimination. That was a bitter moment, but the fact that we kicked on from half-time and despite the red card showed belief."
If Germany were to finish second, and Brazil were to win their group, there will be a repeat of the 2002 final in the Round of 16. Brazil won 2-0 16 years ago.