Klaebo crossed the line in 3:29.46 to finish ahead of his compatriots Paal Golberg and Erik Valnes, who claimed second and third respectively to make it a Norwegian one-two-three.
The victory for Klaebo helps him close the gap on Alexander Bolshunov at the top of the overall World Cup standings, with the Russian only able to finish seventh.
In the women's event, Russian skier Natalia Nepryaeva claimed her second cross-country World Cup victory and her first in a sprint race with a sterling display in Oberstdorf.
The 24-year-old Olympic bronze medallist crossed the line in 3:27.08 in the final as she finished ahead of Slovakian Anamarija Lampic, who settled for second.
American Jessica Diggins completed the podium after edging out her compatriot Sophie Cadwell but it was Nepryaeva's day as she moved up to second on the World Cup overall standings.
Her victory increases her points total to 1087, overtaking Norwegian Heidi Weng (1020) to move into second, although Therese Johaug still leads the way on 1553 points.