The 12th-seeded Klaasen and American Butorac were beaten 6-3 7-6 (4) at the quarterfinal stage at Flushing Meadows by the unheralded US pairing of Rajeev Ram and Scott Lipsky.
There was only one break of service in the entire 1hr 48min match, with Butorac faltering on his deliveries in the opening set.
While the South African-US duo saved five match points in the second set, the dominant all-round play of Ram, who is better known for his singles achievements, and the consistent serves of 33-year-old veteran Lipsky gave them an edge in qualifying for their first grand slam semi-final.
Klaasen and Butorac, in the process, missed out on a repeat grand slam clash against the top seeds and world number couple of Bob and Mike Bryan, whom they had beaten in the Australian Open in Melbourne in January.
Compensation for the 23rd world-ranked Klaasen, however, is that in reaching the quarterfinals of the US Open, he will probably surpass his best-ever world ranking of 22, and possibly make it into the top 20 for the first time.
Also, sweetening the loss is a tidy some of more than R330 000 in prize money for reaching the quarterfinals.