With his first touch two minutes after coming on, Klose poked home at the back post from a Toni Kroos corner in the 71st minute to move level with former Brazil striker Ronaldo.
He becomes only the third man after compatriot Uwe Seeler and Brazil’s Pele to score in four World Cups.
“Twenty (World Cup) matches and 15 goals is not bad at all,” Klose said. “But what’s important is that we have a good match against the United States.”