The 25 metre thunderbolt came with 20 minutes left and gave the hosts an advantage they barely deserved after England had dominated large parts of play.
"The way it finished up was like in a film," said Podolski. "I am proud of the last 13 years in the national team. "It was a great game, a great result and a great way to say goodbye."
The victory was also sweet for the Germany head coach Joachim Loew. The hosts registered a record seventh game without conceding a goal - a run that started after their Euro 2016 semi-final defeat to France.
The success came with Loew missing several regulars such as skipper and goalkeeper Manuel Neuer, defender Jerome Boateng, midfielders Sami Khedira, Mesut Ozil and Marco Reus as well as forward Mario Gomez.
"Normally fairytales don't happen in football but that was one for him," said England manager Gareth Southgate of Podolski's goal. "It's an outstanding achievement in terms of the goals and caps he has. It was an incredible strike."
Podolski made his debut in 2004 and was a constant member of the national squad since Loew took sole charge of the team after the 2006 World Cup in Germany.
"The goal was typically 'Poldi'," said Loew. "But special players deserve a special farewell like this, which was great for him. We had thought of taking him off earlier. But he said during half-time that he wanted to play as long as possible."
Both Toni Kroos and Thomas Mueller, who came off the bench, agreed that Podolski's farewell could not have been scripted better. "Things like that only happen in football," said Kroos. "Against a backdrop like that came a goal like that - unbelievable. "That wasn't a goal they gifted to us. It was a lovely thing for Lukas."
Mueller said it was a fitting end to a spectacular career. "I could not have written a better screenplay, even if it was a bit too cheesy for me as a director," he quipped. "It wasn't an unusual goal for him and it's right that he should soak up the moment and enjoy it.
"Normally, a stadium is empty 10 minutes after the end of a match. But this time everyone wanted to see Lukas.
"If you have played 130 internationals, you have to have had something special."