The Monaco star — who is expected to complete his 88 million-euro move to Real Madrid this week — controlled a looped header from Juan Cuadrado with his chest before turning and volleying home via the underside of the crossbar from 20 yards out to give Jose Pekerman's men the lead after 28 minutes of play.
WORLD CUP: Beautiful people | Germany homecoming
James doubled his tally with a tap-in from close range after the break to help Colombia to a quarterfinal meeting with Brazil, which it would eventually lose 2-1.
The 23-year-old was one of the undisputed stars of the tournament and netted six goals in five games to scoop up the Golden Boot award ahead of Germany forward Thomas Muller.
James becomes the third straight South American winner of the goal of the World Cup award, which is organized by FIFA's official website, with Argentina’s Maxi Rodriguez having triumphed in 2006 and Diego Forlan collecting the trophy four years later.