The Swiss superstar remains two Grand Slam singles crowns shy of Pete Sampras' all-time record of 14 as he tries to become the first player since Bill Tilden in 1924 to win five US titles in a row.
Federer's win streak at Flushing Meadows since losing to David Nalbandian in the round of 16 in 2003 does not include a fourth-round walkover in 2004. He has not fallen short of the fourth round at a Slam since the 2004 French Open.
Second seed Federer was bumped from the world number one ranking by Spain's Rafael Nadal two weeks ago after the Spaniard had beaten Federer in the French Open and Wimbledon finals earlier this year.
Never in tennis history have players met in the finals of three consecutive Slams in the same year.
Stepanek was denied his first trip to the US Open's fourth round, falling to 2-10 in the third round at Slams even though he had beaten Federer in their most recent prior meeting in the Rome quarter-finals.
Federer will next face the winner of a later match between Russia's Igor Andreev and Spanish 13th seed Fernando Verdasco.
Russian fifth seed Nikolay Davydenko, who lost to Federer in the US Open semi-finals each of the past two years, also reached the round of 16 by defeating 27th-ranked compatriot Dmitry Tursunov 6-2, 7-6 (7/3), 6-3.
Davydenko next faces Luxembourg qualifier Gilles Muller, who outlasted Spain's Nicolas Almagro 6-7 (3/7), 3-6, 7-6 (7/5), 7-6 (7/4), 7-5.
Since winning his 14th career title in June at Warsaw, Davydenko had lost four of six matches before the Open. But he has found top form again and could face the Federer express again in this year's quarter-finals.
"I'm not top fit but I need to do everything to be top fit, fight every point," Davydenko said. "I'm really happy to win three rounds in three sets. I hope I will be fit and feeling good for the fourth round."
Serbian third seed Novak Djokovic, who lost to Federer in the 2007 US Open final, meets Croatia's Marin Cilic in a night match at Arthur Ashe Stadium, where US eighth seed Andy Roddick and Italy's Andreas Steppi also meet later.
Federer's win streak at Flushing Meadows since losing to David Nalbandian in the round of 16 in 2003 does not include a fourth-round walkover in 2004. He has not fallen short of the fourth round at a Slam since the 2004 French Open.
Second seed Federer was bumped from the world number one ranking by Spain's Rafael Nadal two weeks ago after the Spaniard had beaten Federer in the French Open and Wimbledon finals earlier this year.
Never in tennis history have players met in the finals of three consecutive Slams in the same year.
Stepanek was denied his first trip to the US Open's fourth round, falling to 2-10 in the third round at Slams even though he had beaten Federer in their most recent prior meeting in the Rome quarter-finals.
Federer will next face the winner of a later match between Russia's Igor Andreev and Spanish 13th seed Fernando Verdasco.
Russian fifth seed Nikolay Davydenko, who lost to Federer in the US Open semi-finals each of the past two years, also reached the round of 16 by defeating 27th-ranked compatriot Dmitry Tursunov 6-2, 7-6 (7/3), 6-3.
Davydenko next faces Luxembourg qualifier Gilles Muller, who outlasted Spain's Nicolas Almagro 6-7 (3/7), 3-6, 7-6 (7/5), 7-6 (7/4), 7-5.
Since winning his 14th career title in June at Warsaw, Davydenko had lost four of six matches before the Open. But he has found top form again and could face the Federer express again in this year's quarter-finals.
"I'm not top fit but I need to do everything to be top fit, fight every point," Davydenko said. "I'm really happy to win three rounds in three sets. I hope I will be fit and feeling good for the fourth round."
Serbian third seed Novak Djokovic, who lost to Federer in the 2007 US Open final, meets Croatia's Marin Cilic in a night match at Arthur Ashe Stadium, where US eighth seed Andy Roddick and Italy's Andreas Steppi also meet later.
by Jim Slater