Brabham won by 43 seconds over the Cooper T81 driven by 1964 World Champion John Surtees.
The race also saw the death of British driver John Taylor after a collision with Jacky Ickx.
Brabham had collected 39 points, more than double his nearest rival, BRM driver Graham Hill.
Jim Clark, despite qualifying on pole, made a mistake and spun into a ditch after using the wrong tyres.
This would be the last Formula One race on the original Nürburgring Nordschleife before the Hohenrain chicane was added to slow the cars coming into the pits.