Mario Goetze nodded Germany ahead in the 51st minute, but Ghana instantly roared into attack. Andre Ayew headed an excellent equaliser three minutes later, and the Ghanaians went ahead when a great interception and pass by Sulley Muntari set up Asamoah Gyan to lash home in the 63rd.
Germany levelled in the 71st minute with a sharp finish by Klose as the substitute claimed his 15th World Cup goal to move level with former Brazil striker Ronaldo as the tournament's all-time leading scorer.
Germany, who crushed Portugal 4-0 in their opening game, have four points. The United States have three, Ghana one and Portual zero ahead of their Group G game against the U.S. on Sunday.