"It hasn't been easy, but this is life. You know, life gives you things [but also] takes away close people," Djokovic said. "We were very close throughout my whole life, and she taught me a lot of things that are part of me, part of my character."
Gencic connected with a 6-year-old Novak at a tennis camp, then worked with him for five years.
"I feel even more responsible now to go all the way in this tournament," said the No. 1-ranked Djokovic, who owns six Grand Slam titles but none from Roland Garros. "I want to do it for her."
He'll need to beat three more opponents to accomplish that, starting with 12th-seeded Tommy Haas, who at 35 became the oldest French Open quarterfinalist since 1971 by eliminating Mikhail Youzhny 6-1, 6-1, 6-3 in less than 1½ hours.
If Djokovic can get past Haas, he could find a familiar foe in the semifinals: seven-time French Open champion Rafael Nadal, who played his first relatively routine opening set of the tournament and put together a 6-4, 6-1, 6-3 victory over No. 13 Kei Nishikori of Japan.
Nadal, who beat Djokovic in last year's final and is 56-1 in his French Open career, declared: "I played much better today than the first three matches. No doubt about that."
Consider that something of a warning for No. 9 Stanislas Wawrinka, who edged No. 7 Richard Gasquet 6-7 (5), 4-6, 6-4, 7-5, 8-6.
Maria Sharapova, the women's defending champion, moved into the quarterfinals by beating 17th-seeded Sloane Stephens of the United States 6-4, 6-3, part of a rough day for Americans.
The other two in action also exited in straight sets: 54th-ranked Jamie Hampton lost to 18th-seeded Jelena Jankovic 6-0, 6-2, and 67th-ranked Bethanie Mattek-Sands was beaten by 12th-seeded Maria Kirilenko 7-5, 6-4. Kirilenko now meets two-time Australian Open champion Victoria Azarenka, a 6-3, 6-0 winner over 2010 French Open titlist Francesca Schiavone.
P Quarterfinals, Tuesday, 11 a.m. (tape), ESPN2