Klosterhalfen, who led the race from the gun, clocked an impressive 14:26.76 to break 20-year-old Irina Mikitenko's German record of 14:42.03.
"I wanted to run as fast as I can:" Klosterhalfen told ARD sports.
The 22-year-old Klosterhalfen lapped every runner in the race except Alina Reh, who took silver at with 15:19.42.
Klosterhalfen moves to fourth on the European all-time list ahead of Great Britain’s Paula Radcliffe.
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