Wales' faint Euro 2008 qualification hopes were realistically ended by Germany as the Group D leaders punished the home side's mistakes in Cardiff.
Wales made a terrible start as Klose scored after five minutes
Miroslav Klose put the visitors ahead with just five minutes on the clock after Jason Koumas had lost possession.
Gareth Bale's hesitancy then cost Wales after the break as captain Klose headed in from Roberto Hilbert's cross.
Klose could have scored twice more in the final stages, as Wales' only shot on target came from Sam Ricketts.
The Germans have now virtually guaranteed their place in next year's finals as they lead the group having picked up 22 points from a possible 24.
Wales are now 10 points adrift of second-place Czech Republic with five games left to play, only one of which will be at home.
Welsh hopes of a result took a significant blow when captain Craig Bellamy withdrew from the side because of concerns over his new-born baby daughter.
And their task became even harder when Klose pounced in the opening stages to put the run-away Group D leaders ahead.
Koumas, who manager John Toshack had identified as his main playmaker now Ryan Giggs has retired, lost the ball inside his own half, giving striker Kevin Kuranyi a clear run at the retreating Wales defence.
His pass was perfectly weighted into Klose's path and the captain's first-time strike with the outside of his right foot found the bottom corner.
Germany began to seize complete control and the home side need a superb last-ditch lunge by Lewin Nyatanga to stop Kuranyi from doubling the lead on 23 minutes.
The tall striker had been put through by a deft touch by Bastian Schweinsteiger, who pulled the strings all evening in Germany's midfield.
Kuranyi was again denied as the half drew to a close when James Collins blocked his shot inside the box after Wales were again guilty of giving the ball away cheaply.
Jason Koumas failed to make in impact in midfield
Lone striker Freddy Eastwood endured a difficult first-half on his home debut, but the Wolves striker finally got his first sight on goal just before the break when his far-post header was blocked for a corner.
Robert Earnshaw was sent on for the second half to give Eastwood more support, and the change seemed to give Wales more attacking impetus.
Germany, though, slowly started to reassert their authority and Wales goalkeeper Wayne Hennessey was called into action twice in quick succession.
The excellent Schweinsteiger then shaved the crossbar with a beautiful curling effort, but the game was over as a contest moments later when Klose struck again.
Bale was the culprit this time as he was robbed on the right flank by Roberto Hilbert, and his perfect chipped cross was headed in by Klose.
The German captain then had two excellent chances to complete his hat-tick.
He first fired straight at Hennessey, who again showed composure beyond his 20 years, and then sent a free header wide of the post.
Wales kept pressing until the final whistle, but their limited attacking ideas were easily snuffed out, leaving Toshack with a tough task to lift his players before Wednesday's visit to Slovakia.
Wales: Hennessey, Ricketts, Gabbidon, James Collins, Nyatanga, Ledley (Earnshaw 46), Bale, Koumas (Fletcher 67), Robinson, Davies (Crofts 79), Eastwood.
Subs Not Used: Price, Morgan, Llewellyn, Jones.
Booked: Gabbidon, James Collins.
Germany: Lehmann, Arne Friedrich, Mertesacker, Metzelder, Pander (Trochowski 46), Hilbert, Hitzlsperger, Schweinsteiger, Jansen, Kuranyi (Podolski 72), Klose (Helmes 87).
Subs Not Used: Hildebrand, Odonkor, Manuel Friedrich, Rolfes.
Goals: Klose 5, 60.
Ref: Manuel Enrique Mejuto Gonzalez (Spain).