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 in Fortaleza.
But Klose had the last laugh with a poacher's goal just 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.
German captain Phillip Lahm refused to use the sweltering conditions as a reason for their performance.
"It was a gruelling 90 minutes, the weather can't be an excuse, we were not as aggressive and gave them too much room," said Lahm, who like several of the squad have experienced semi-final heartbreak in 2006 and 2010.
"We had the better chances, but overall we can't be satisfied."
Gyan, whose goal saw him join Cameroon legend Roger Milla as the leading all-time African scorer with five, said that they had played much better than in the 2-1 defeat to the United States.
"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."
With the USA playing Portugal in Manaus on Sunday, the result breathes life back into Ghana's hopes of reaching the last 16.
The Germans could be knocked from top of the group and must beat Jurgen Klinsmann's Stars and Stripes in Recife on Thursday to be sure of reaching the knock-out stages.
Having at times bossed the first half, and only been denied by two fantastic Manuel Neuer saves from Sulley Muntari and Christian Atsu, Ghana switched off at the start of the second.
Thomas Mueller picked out Goetze running into the box and the Bayern Munich midfielder mistimed his header, but the ball went in off his knee before rebounding past Ghana goalkeeper Abdul-Fatawu Dauda.
The lead lasted only three minutes.
Harrison Afful crossed into the box and Ayew, on his 50th appearance for the Black Stars, climbed above Shkodran Mustafi and the static Per Mertesacker, playing his 100th game for Germany, to flick a header beyond Neuer.
Nine minutes later things got even better for Ghana as Muntari dispossessed Germany captain Philipp Lahm in midfield and slid the ball through to Black Stars captain Gyan to smash the ball past Neuer.
The Black Stars broke out in some impressive dance moves in celebration wafter Gyan's goal.
Ghana were running riot and Germany were just hanging on, but an inspired substitution by coach Joachim Loew brought Klose into the fray to stab home from a yard out after Benedikt Hoewedes flicked on Toni Kroos's corner.
Both sides had late chances to win the game as Jordan Ayew headed over with the German defence again all at sea.
At the other end, only a superb Kwadwo Asamoah tackle denied Mueller before Ozil also went close, while Gyan pulled a late shot wide in a frantic finish.
Mueller required extensive treatment for a cut over an eye at the final whistle, after crashing into centre-back John Boye, but should be fit to face the USA.
Jerome Boateng has a thigh injury and Loew has said he hopes to have the Bayern Munich defender fit for the America clash.
Kevin-Prince Boateng, who has failed to have the impact he had in the 2010 finals, said that a draw had been a fair result.
"We had set out to win today, but we should be happy with the result," said Ghana's Kevin-Prince Boateng.
"It went backwards and forwards, Germany could have won it, we could have won it – the point was fair.
"We didn't want to let them get into the game, that was the key today."