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."
Germany, who are top of the group with four points, face the Americans in their final group match in Recife on Thursday while Ghana, with one point, play Portugal in Brasilia.
The United States (three points) take on bottom-side Portugal in their second match on Sunday.
Germany coach Joachim Loew said his players were "exhausted" from an engrossing encounter in which the Germans took the lead, trailed 2-1 before fighting back to secure a point.
"Ghana did a good job. They succeeded in closing down space, we weren't able to get the open spaces. It was an incredible high pace and the players gave everything," he said.
"We wanted to avoid a hard fight with these temperatures. The team showed a strong morale to come back after we were down."
Ghana coach Kwesi Appiah described the clash as "a really good, competitive game."
"Germany are the best in the world and playing them is always going to be difficult. We had some opportunities and unfortunately when you're playing such a big team, if you don’t take your chances, you're always going to face problems."
After a cagey, goalless first half, Mario Goezte put the Germans ahead with a downward header that came off his knee before beating Fatawu Dauda in the Ghanaian goal.
But the Africans hit back three minutes later, Andre Ayew outleaping the towering figure of Per Mertesacker in the German defence to meet a Harrison Afful cross and head his side level.
Roared on by thousands of Brazilians in Fortaleza's Castelao arena, Ghana then took the lead, their lone striker Asamoah Gyan breaching the German back line and firing a right foot shot past goalkeeper Manuel Neuer.
Loew then turned to experience, throwing on Klose and Bastian Schweinsteiger and it proved an inspired switch with Klose netting the goal that keeps the Germans in contention to reach the second round for a remarkable 16th consecutive World Cup.
The 36-year-old celebrated his goal with a somersault, reminiscent of his younger days. He landed on his backside but it hardly seemed to matter as his jubilant team mates buried him under a pile of bodies.
This was the 800th match in the tournament's history and was a fitting tribute to an event that began in 1930.
It marked Mertesacker's 100th German cap and Gyan's 10th World Cup match, a Ghanaian record.
It also saw the Boateng half-brothers face each other for the second World Cup in a row. Jerome played the first half for Germany while Kevin-Prince played for Ghana.
(editing by Justin Palmer)
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