Podolski was under fire for failing to contribute to Germany's attacking game in the previous two matches but said it was on coach Joachim Low's orders to operate deeper.
He delivered on that promise to give Germany the lead in the 19th minute, rifling in from close range for his 44th international goal.
"It was something special for me that I got a goal in my 100th match," Podolski told German televsion.
"The most important thing is that we won. It was a tough match against a strong Denmark team and fortunately we got the second goal and won it.
"We had three matches and three wins and now we'll prepare for [a quarter-final against] Greece."
"Prince Poldi", as he is known in his hometown of Cologne, won his first cap in 2004 and has since put a reserve sign on the German right wing. He will display his skills for Arsenal in England's Premier League next season.
Competing in his fifth major tournament, the 27-year-old, had failed to shine on the right, showing only a few of his trademark darting runs.
On Sunday, however, he made amends when a low Thomas Muller cross was flicked on by Mario Gomez and Podolski fired in.
A little later he could have added another but his sizzling free kick buzzed narrowly over the bar.
He was substituted in the 64th minute, hearing his name chanted by 12,000 Germany fans for the first time in the tournament and he was later awarded man of the match.
