The British world number three failed to break the Argentine during the three-set contest as his hopes of claiming the world number two spot were thwarted.
Both players held serve throughout the opening set before Murray gained the initiative by seeing out the tie-break 7-5.
However, the Scot began to labour in the second and Del Potro took advantage with a single break on his way to levelling the match 6-3.
The world number seven broke twice in the deciding set on his way to a 4-1 lead before a double fault from Murray saw him close out the match 6-1.
Del Potro's reward for beating Murray is a semi-final encounter with world number one Novak Djokovic.