Del Potro, the 2009 US Open champion, has been working to recover his best form after wrist surgery in 2010.
"I'm into another semi-final, this is important for my year and my progress. To beat Haas indoors is a good win," said the Argentine.
"Tommy is dangerous. If you don't focus against him you can make mistakes. I was able to close it out well with my serve. But I need to play better if I'm to get any further."
Del Potro, who will lead his nation against Spain in the December 2-4 Davis Cup final in Seville, next faces either home star, and two-time champion, Jurgen Melzer or South African sixth seed Kevin Anderson.
Haas, 33, who underwent hip surgery in 2010, was playing in his first quarter-final in more than two years as his own recovery continues and had to qualify for the main draw.
Del Potro still has a chance of claiming one of the eight places in the year-ending ATP World Tour Finals in London next month.
He stands provisional 12th in the race, with three spots in the eight-man field still open and only two more weeks to go in the regular ATP season.
Del Potro defeated Haas in 80 minutes with 10 aces and three breaks of serve.
Former number two Haas never managed a break point against the South American who has won titles this season at Delray Beach and Estoril.
Del Potro's win was his 44th of the season.
"The Davis Cup is on our minds every day," admitted Del Potro. "But I'm a professional and it's this week that I'm concentrating on."
"Then there's Valencia, Paris and then the Davis Cup. The Davis Cup is the goal but there are important tournaments before that."
The Argentine reached his last final at Estoril in April, where he beat Spain's Fernando Verdasco in the build-up to the French Open.
Del Potro powers past Haas in Vienna
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