The 36-year-old, who also became only the third player to score in four different World Cups, stepped off the bench to equalise from close range following a Toni Kroos corner.
Mario Gotze had put Joachim Low’s side ahead just after the break, but goals from Andre Ayew and Asamoah Gyan put Ghana into an unlikely lead.
Despite a spirited showing from Ghana, Klose’s goal stole all of the headlines from Kwesi Appiah’s men and he is now hoping to become the competition’s outright top scorer.
"It's a pleasure to equal Ronaldo's record, he is a great striker and person. I hope to play more times and score other goals in this World Cup," he told Globo after the game.
"Twenty (World Cup) matches and 15 goals is not bad at all.
"But what's important is that we have a good match against the United States (on Thursday)."
Meanwhile, Ronaldo himself posted on his official Twitter account to acknowledge Klose’s achievement: "Welcome to the club #Klose."
Germany boss Joachim Low cut a frustrated figure on the touchlines at times during the second half, but he saluted Ghana’s spirit at full-time.
"Ghana did a good job. They succeeded in closing down space, we weren't able to get the open spaces," he said.
"It was an incredible high pace and the players gave everything.
"We wanted to avoid a hard fight with these temperatures. The team showed a strong morale to come back after we were down."