The 32-year-old qualifier produced a quite sensational performance here yesterday, sending No.2 seed Simona Halep, a pre-tournament favourite, out with a brilliant 7-6, 6-2 triumph.
If that is not startling enough, the way her life was turned upside down by her abusive father, Marinko, who forced Lucic-Baroni to flee Croatia and move to the United States in 1999 - a year before she reached the Wimbledon semi-final only to lose to Steffi Graf in a match she really should have won - is staggering and remarkable in equal measure.
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Such an awful situation naturally hampered what was shaping up to be a highly promising tennis career. Indeed, she took herself out of the sport in 2003 and played only two tournaments in the 2004, 2005, and 2006 seasons combined.
Yesterday, though, was a triumph against all the odds and a win no-one would begrudge her.
An emotional Lucic-Baroni said: "It's been really hard. Sorry. After so many years, to be here again, it's incredible. I wanted this so bad. So many times I would get to a place where I could do it. Then I wanted it so bad that I'm kind of burned out.
"I feel like I'm 15. It's crazy. I'm 32, but I don't feel like that. My body is really great. I feel fit. I feel strong in my mind. I still have so much desire. It is the best day of my life."
For Halep, there was only acute disappointment. "I wasn't in a good mood after losing a set from 5-2 and I tried everything I could. I don't know much about her career but she played well and I wish her luck."
Another player who has failed to build on his huge potential is Bernard Tomic and the Australian's miserable year continued last night when the world No.67 was forced to pull out of his second-round match with David Ferrer because of a hip injury.