It was the biggest win of Yuki's career when the third seed formidable Italian, who struggled due to an injured left leg, conceded the match after trailing 1-6 5-5.
Fognini had earlier pulled out of the doubles event for which he was supposed to partner India's veteran star Leander Paes. They duo were seeded second.
The 21-year-old Indian, ranked 195, is only the third Indian after Somdev Devvarman and Leander Paes to make the singles quarterfinals of this event in Chennai.
Somdev had ended runner-up in the 2009 edition. Paes had reached the semifinal in 1998 when the event was known as Gold Flake Open. Paes had lost to eventual champion Patrick Rafter from Australia.
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19-year-old Chennai boy Ramkumar, who came through qualfiers and shocked Somdev in the first round, put up a brave fight against world number 38 Marcel Granollers before losing his second round encounter 2-6 4-6.
Despite his restricted movements, Fognini was good enough to trouble Yuki with his solid ground strokes, specifically his power-packed forehand.