Novak Djokovic was severely tested before securing a 6-3, 4-6, 6-4 win over Philipp Kohlschreiber.
Novak Djokovic was playing his first tournament since lifting a record seventh title in Melbourne, taking his tally of Grand Slam victories to 15.
Rafael Nadal, a 14-time Grand Slam champion, is now just one win away from matching Argentine legend Guillermo Vilas's record of 49 clay-court titles.
Philipp Kohlschreiber stunned second seed Marin Cilic 3-6, 6-3, 6-4 on Friday to move into the semi-finals of the Rotterdam World Tennis
Seventh seed Kei Nishikori of Japan brushed aside Philipp Kohlschreiber in straight sets to make a winning start in the 2016 Australian Open.
Six-time champion Roger Federer overcame Philipp Kohlschreiber 6-4, 4-6, 6-4 and will face Belgium's David Goffin in quarters.
Roger Federer defeated Germany's Philipp Kohlschreiber for the 10th time in 10 meetings.
Novak Djokovic cruised to a straight sets win against Germany's Philipp Kohlschreiber to advance in Paris Masters.
Eighth-seeded David Goffin of Belgium next plays Germany's Jan-Lennard Struff for the first time. Struff advanced after third-seeded Philipp Kohlschreiber retired when trailing 5-0 after just 20 minutes.
Thirteenth-seeded American John Isner was beaten 7-6 (4), 4-6, 7-6 (2), 7-6 (4) by Germany's Philipp Kohlschreiber.
John Isner, who is America's highest-ranked man at the tournament, has a 4-2 winning record over Philipp Kohlschreiber but the two losses both came at Flushing Meadows with the German winning in five sets in 2012 and four sets last year.
Tommy Haas' hopes of making the ATP World Tour Finals in London was dented when he lost to Philipp Kohlschreiber in the first round of the Valencia Open. Haas lies 12th in the race to London standings.
The second-seeded Nadal, who counts the 2010 U.S. Open among his 12 Grand Slam titles, beat Kohlschreiber on Monday night in the fourth round.
Fognini led 4-1 before dropping serve in the third. He held on and became the first Italian champion in Stuttgart.
He is making his 13th appearance at the pre-Wimbledon warm-up and took the title for the first time in 2012, beating Roger Federer in the final.
Top seed Novak Djokovic reached the French Open quarter-finals on Monday with a 4-6, 6-3, 6-4, 6-4 win over German 16th seed Philipp Kohlschreiber.
He has also won 34 of his 36 matches on clay in 2013 -- he lost to Horacio Zeballos in his first tournament back at Vina del Mar in February before seeing his eight-year winning streak at Monte Carlo ended by Djokovic in April.
Nadal holds a perfect 9-0 record over Almagro and has already beaten his compatriot this season in an Acapulco semi-final.