Živojinović represented SFR Yugoslavia as the number 15 seed at the 1988 Summer Olympics in Seoul, where he was defeated in the second round by France's Guy Forget.
The right-hander won two career singles titles (Houston, 1986 and Sydney, 1988), as well as eight doubles titles. He reached his highest singles ATP ranking on 26 October 1987, when he became world No. 19. Živojinović was known for his tall, wiry frame that made him the original big-boom server before Goran Ivanisevic.[5] He built his game on his big serve, enhanced greatly by his height and his muscular thighs. He was an exciting player to watch and a very troubling one to play against. His ace total in a match often became difficult to overcome, with the result that no one looked forward to playing against him.[6]
Živojinović's most notable Grand Slam results were two semifinals. As an unseeded player at the 1985 Australian Open, he memorably beat John McEnroe in a five-set quarterfinal to reach the semifinals (where he lost in straight sets to Mats Wilander). The next year, at the 1986 Wimbledon semifinal, again as an unseeded player, he lost to Ivan Lendl in a five-set match.
Over the course of his career, Živojinović amassed an overall singles record of 150 wins and 138 defeats. He was much more successful in doubles competition, winning the US Open in 1986 with Andrés Gómez. The same year, he won three more tournaments. He was ranked as the world No. 1 doubles player on 8 September 1986.
In the early-to-mid 1980s, active professional tennis player Živojinović became engaged to Zorica Desnica.[7] The couple had a son, Filip, in 1985.[7] They split up during the late 1980s.
In October 1989, twenty-six-year-old Živojinović began dating the Yugoslav folk superstar Lepa Brena, nearly three years his senior, having reportedly met her at the premiere of her star vehicle movie Hajde da se volimo 2 [sr].[8] Their 7 December 1991 wedding—a lavish ceremony at Belgrade's InterContinental Hotel with tennis player Ion Țiriac as the groom's best man—was a media event throughout Yugoslavia.[9] The level of attention it generated in the country was such that Brena's managerRaka Đokić [sr] released a VHS tape of the wedding for commercial exploitation.[10]
The couple's child, son Stefan Emerald Živojinović, was born in May 1992 in New York City.[11] Their second son, Viktor Ernest Živojinović, was born in March 1998 in Miami.[11] On 23 November 2000, eight-year-old Stefan was kidnapped by the Zemun Clan in front of the family's home in Belgrade. He was released five days later and left on the side of a highway after his family paid a ransom reported to be more than DM2 million.[12]