Vukasin Ziramov, 25, died last week after jumping off a bridge into a river while on an outing with friends in Senta.
"It's been very sad news," Ivanovic, the 13th seed at Flushing Meadows, said after her 6-2 6-0 rout of Anna Tatishvili of Georgia.
"It was very hard because it was almost like my relative. We grew up, and I knew him since we were kids. It's very, very sad."
On the court, Ivanovic showed the positive effects of working with a new Serbian conditioning and coaching team she took on after Wimbledon as she works her way back after a disappointing stretch in her career.
The 25-year-old Serb, who rose to the top ranking in women's tennis in 2008 after winning the French Open, had dropped to 22 in the rankings in 2011.
Ivanovic ranked 15th heading to Flushing Meadows.
"I was playing really well and I had a few tough losses," Ivanovic said about a hardcourt build-up that included a three-set loss to Victoria Azarenka in Carlsbad, a third-set tiebreaker loss to China's Li Na in Toronto and a three-set loss France's Alize Cornet in Cincinnati.
"I'm very confident with the game and the way I was playing," she said, adding she was concentrating on conditioning and making her serve and forehand more dominant.
Ivanovic said she was driven to return to the upper echelon of the game.
"It's my only goal I have at the moment," she said. "I really want to get back to the top of the game. I believe I have qualities to do so.
"Once you're in the top, you don't really feel satisfied with being in the top 15. You really want to aim and push yourself. That's where I am at. I really want to put my head down and work hard and try to maximize my potential."
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