Bulgaria and the Netherlands also posted impressive shutout victories Wednesday to put themselves well on course for places in the 1996 finals in England.
The Bulgarians strolled to a 3-0 victory in Wales and the Dutch marked Dick Advocaat's final game in charge with a 5-0 crushing of soccer minnow Luxembourg.
Germany, which also plays Albania at home on Sunday, posted its second victory from two games with Klinsmann scoring and setting up goals for Ulf Kirsten and Lothar Matthaeus.
Some 20,000 fans crammed into the 18,000-seater Kishinev stadium to see the Germans dominate and return to far better form than they showed in the summer when they surrendered the World Cup.
The Germans cruised into a 2-0 lead by the 38th minute. Kirsten fired them ahead after seven with a header from Klinsmann's center and Klinsmann added the second with a low shot. Klinsmann also set up Germany's third in the 72nd minute, heading a center down to Matthaeus who fired the ball home from close range.
"I am happy again after a long, long time," said Berti Vogts, after his 50th game as German coach. "We clearly dominated for long periods. We are moving in the right direction."
Trifon Ivanov and Emil Kostadinov fired the Bulgarians into a 2-0 lead by the 15th minute in Cardiff and Barcelona star Hristo Stoichkov netted the third six minutes after half time.
The Bulgarians top the Group Seven standings with nine points with the Germans, Georgia and Moldova all with six. The Welsh, who have conceded 11 goals in three successive defeats, have three and virtually no chances of playing in England in two years time.
Against Wales, Bulgarian defender Trifon Ivanov moved up to fire his team ahead in the fifth minute with a volley from 20 yards before Emil Kostadinov robbed a Welsh defender and fired the second in the 15th. But for a series of saves by veteran Welsh goalkeeper Neville Southall the Bulgarians would have doubled that lead by half time, but Hristo Stoichkov rounded him to score the third in the 51st minute.
Georgia, which whipped Wales 5-0 in its previous game, gained a 1-0 victory at Albania.
Switzerland moved three points clear atop the Group Three standings after winning 2-1 at Turkey.
Israel held World Cup quarterfinalist Romania to a 1-1 tie in Tel Aviv in a meeting of the two teams atop Group One. Both teams have eight points and the Romanians remain top on goal difference.
Norway, which failed to impress at the World Cup, gained a 1-0 victory in Malta to stay top of Group Five with 10 points from four games. Jan-Aage Fjortoft , who also plays in England for Division One Swindon, scored the goal.
The Finns now have six points, one behind second place Scotland but three behind Greece.
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