The Swedish fifth seed, who ended Federer's run of 23 Grand Slam semi-finals in a row with a French Open quarter-final upset, defeated 48th-ranked Dutchman Thiemo de Bakker 6-2, 6-3, 6-3 in brisk winds after one hour and 42 minutes.
"It was very tough. I was fighting the wind the whole time. During these conditions I played a pretty good match," Soderling said. "It's great to make it to the second week at the US Open. It will be very big next week."
Soderling will play for a berth in the quarter-finals against Spanish 21st seed Albert Montanes, who led 6-2, 2-1 when 147th-ranked Japanese qualifier Kei Nishikori retired after only 38 minutes with a groin injury.
"He was not well physically so that was lucky for me," Montanes said. "I realized he was very flat. He was not moving. I tried not to think of that but he was moving quite slowly."
Federer, a 16-time Grand Slam champion, was to face France's 109th-ranked Paul-Henri Mathieu and Serbian third seed Novak Djokovic was set to play 108th-rated US wildcard James Blake in later matches at Arthur Ashe Stadium.
Five-time US Open winner Federer and Soderling, who lost the French Open final to world number one Rafael Nadal, are on a collision course with added drama after Soderling's lone victory in 13 meetings with the Swiss star.
"Everybody has been telling me since the draw came out I'm playing Roger in the quarters. It's still far ahead," Soderling said.
"It's always difficult to play against Roger and I have played him a lot of times. In any tournament they play, Roger and Rafa will be the favorites, but there are a lot of players who can beat them."
Soderling, whose best US Open showing was last year's quarter-final run, made 30 winners and only 19 unforced errors.
Nishikori, 20, was coming off an exhausting five-set upset of Croatian 11th seed Marin Cilic. Another victory would have matched his 2008 run to the fourth round as the best US Open showing by a Japanese man since 1937.
"I began to feel it in warmups," Nishikori said. "I could not finish the tennis match."
Montanes, 29, claimed his first spot in the fourth round in 36 Grand Slam appearances. He is among nine Spaniards to reach the third round, the most at any Slam tournament in the Open Era.
Monfils, among a US Open record six Frenchman in the third round, matched his best US Open run by reaching the last 16 for the third year in a row. His only win in three prior matches with the Serb was by a retirement last year.
Gasquet, who also equalled his best US Open run from 2005, won four of the last five points in the second-set tie-breaker, the last on a service winner, and broke in the last game of the match for the win.
Anderson, 0-6 in Grand Slam matches before this week, failed to become the first South African man to reach the fourth round at a Slam since Wayne Ferreira's 2003 Australian Open semi-final run.
Source: AFP Global Edition