Mario Goetze had given Germany the lead before goals from Andre Ayew and Asamoah Gyan turned the game on its head and threatened to cause a major upset for the Black Stars.
But Klose had the last laugh with a poacher's goal a yard out 19 minutes from time.
"It doesn't matter whether I play from the start or come off the bench: all games are important and 15 goals in 20 World Cup games isn't bad," said the Lazio striker.
"We believed in ourselves today," the 28-year-old told the BBC. "I think tactically we were perfect today. Now we definitely have to beat Portugal. We will have to focus but we believe we can beat them.