The 23-year-old Argentine, ranked 15th in the world, was too strong for the former world number two, who was playing in his first quarter-final after undergoing hip surgery in February 2010.
Del Potro, who had reached a career-high ranking of four early last year before missing much of 2010 with a wrist injury, raced to a 5-2 lead with near-perfect service games and a staggering first serve percentage of 85 percent.
The German, now rank 273rd after launching his own comeback earlier this year, sunk a forehand into the net on the first set point after yet another thundering serve from Del Potro.
Haas, the 2001 winner in Vienna, improved on his serve in the second set to hold on for a 4-3 lead.
A Haas double fault, however, and another forehand error gave Del Potro his first break in the second set to go 5-4 up.
The Argentine then delivered ace number 10 to carve out his first match point with Haas sinking it into the net.
World number nine Jo-Wilfried Tsonga, also hoping for a spot in the World Tour finals, takes on Belgium's Xavier Malisse for a place in the last four later on Friday.
