The two-time Grand Slam champion, who is returning from a six-month injury layoff, cruised past Delic 6-3, 6-4 despite rain showers that interrupted the match mid-play.
The 26-year-old Russian next takes on 28th-seeded Carlos Moya, who had a first round bye.
Meanwhile, Britain’s number one and two, Andy Murray and Tim Henman, secured passage to the second round after posting solid wins over Greek qualifier Vasilis Mazarakis and American qualifier Donald Young, respectively.
The 18-year-old Murray, who recently won his first ATP title in San Jose, next faces 5th-seeded Nikolay Davydenko while Henman will clash with 23rd-seeded and reigning Masters Series Paris champion, Tomas Berdych.
Other first round winners on Friday include German teenager, Florian Mayer, Sweden’s Robin Soderling, Jose Acasuso of Argentina, Croatia’s Ivo Karlovic and America’s Paul Goldstein.
Super Davenport
On the women’s side, second-seeded Lindsay Davenport stormed into the third round as she crushed fellow American Ashley Harkleroad 6-0, 6-0 in no more than 53 minutes.
Third-seeded Maria Sharapova also advanced to the third round as she ousted America’s Jamea Jackson 6-4, 6-3 after a rain delay.
Davenport next meets her 31st-seeded compatriot Laura Granville, while Sharapova faces another American, Lisa Raymond.
Fifth-seeded Anastasia Myskina, seventh-seeded Anna-Lena Groenefeld, tenth-seeded Dinara Safina and 19th-seeded Martina Hingis were also among the second round winners on Friday.