Veteran striker Klose had only been on the pitch as a substitute for two minutes when he jabbed home the equaliser and joined Brazilian great Ronaldo on top of the all-time scoring charts.
The 36-year-old Lazio striker struck in the 71st minute of a thrilling Group G game at Fortaleza's Castelao Stadium after goals from Andre Ayew and Asamoah Gyan had fired Ghana into a 2-1 lead.
Mario Gotze had given Germany the lead, heading in off his own knee on 51 minutes after a goalless first half.
But Ghana struck back brilliantly, levelling through Ayew's 54th minute header before Asamoah fired the Black Stars into the lead.
The result left the Germans, who beat Portugal 4-0 in their opening match on top of Group G with four points.
Ghana, beaten by the United States in their first game, have one point heading into their final match with Portugal next week.
Earlier, Lionel Messi scored a brilliant injury time winner as Argentina overcame Iran 1-0 to book their place in the last 16 in Belo Horizonte.
Four-time world player of the year Messi curled in a sublime shot from just outside the area in the first minute of stoppage time to break Iranian hearts in the Group F battle.
Argentina captain Messi had been largely anonymous for much of the match as Iran frustrated the South American giants at the Mineirao Stadium.
Iran, with only one win in four appearances at the World Cup, looked to have secured a famous draw.
The Asian minnows might even have snatched victory only to be denied by Argentina keeper Sergio Romero, who pulled off fine second half saves from England-based duo Ashkan Dejagah and Reza Ghoochannejad.
But with the clock ticking down, Messi picked up the ball on the edge of the area and after being granted time to pick his spot, curled in his second goal of the tournament.
The result leaves Argentina assured of a place in the last 16, joining Colombia, Costa Rica, Chile and Holland in the second round.
"We are not showing what we can do, but with a run of games I think we will get there," Messi said of Argentina's form.
"We are the first ones to know we have not reached the level we would like."
Iran's former Portugal coach Carlos Queiroz was fuming however over Serbian referee Milorad Mazic's failure to award his side a first half penalty.
"Messi was fantastic, but the referee wasn't," Queiroz said.
"I don't understand it, he had to have seen it was a penalty. He was five metres away, there is no way he couldn't have seen it."
Nigeria and Bosnia, both desperate for a win to get them back on course behind Argentina in Group F, play in Cuiaba.
Nigeria are currently ahead of their rivals with one point from their draw with Iran earlier this week.
Meanwhile, the World Cup hosts are to boost security around Rio de Janeiro's Maracana Stadium to prevent invasions by ticketless fans, officials said.
Rowdy fans gate-crashed each of the two matches at the iconic stadium so far, raising concerns about security at the venue which will host the July 13 final.
"We are going to establish an extra isolation cordon with mobile fences in the Maracana's sensitive zones and mobilise 600 police in those zones," Rio military police commander Jose Luis Castro told a press conference.