Belgium's Daniel Van Buyten, playing against many Bayern Munich team-mates, lost the ball in his own penalty area early in the second half, allowing Germany's Thomas Muller to feed an unmarked Klose and the reliable German marksman made no mistake.
The drilled strike earned a 53rd international goal for Klose, who has scored 14 of them in his three World Cup finals leaving him one shy of Brazilian Ronaldo's record.
Yet Germany, perhaps still shaking off post-World Cup stiffness after their third-place finish, were slow to shine and came off second best for large stretches of the first half.
For many of the German players it was their first match for their country since their 1-0 loss in South Africa to eventual winners Spain. Germany put out a largely second-string side for their 2-2 friendly draw with Denmark last month.
German coach Joachim Low said the players had only returned to training four weeks ago.
"It took some time to get into our rhythm... after the World Cup was difficult. The players weren't so fresh. But after this match against Belgium I saw the team was hungry and that gives me confidence for the future," he said.
Early on, the young Belgian side refused to sit back and twice forced German keeper Manuel Neuer to save shots from 17-year-old striker Romelu Lukaku and Moussa Dembele.
However, the World Cup semi-finalists dominated after the break and effectively closed down the game after Klose's goal.
Belgium's coach Georges Leekens and his players smarted at the loss, many saying a draw might have been a fairer result.
"The Germans settled it with a gift from us," Leekens said. "They were more professional. We still have something to learn."
However, he said he was encouraged by the passion of his team, with nine of the starters 24 years or younger. Loew was also complimentary about the hosts.
"It is important to win away in Belgium. I think other teams will drop points here," he said.
Belgium, known to their fans as the Red Devils, have now lost eight straight matches against Germany and West Germany since a 0-0 draw in 1982, with their last victory in 1954.
Germany host Azerbaijan on Tuesday. Belgium, who have not qualified for a major championship since the 2002 World Cup, travel to Turkey, who lead group A after a 3-0 opening win over Kazakhstan.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1