As a singles player, he reached the semifinals of the 1985 Australian Open and the 1986 Wimbledon Championships, achieving a career-high ranking of world No.

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.

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).

In October 1989, Živojinović began dating the Yugoslav folk superstar Lepa Brena, 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 manager Raka Đokić [sr] subsequently released a VHS tape of the wedding for commercial exploitation.