Now, the skier who turned her back on her national federation to set up her own racing team is ready to enter the record books.
This weekend, all being well, Maze could become the first Alpine ski racer, man or woman, to surpass 2,000 World Cup points in a single season.
The feat would eclipse even the great Hermann Maier - "the Herminator" - whose record of 2,000 has stood for 13 years.
The 29-year-old Maze has reached 1,844 so far, and has already secured her first overall World Cup and the trophy for the best giant slalom skier of the season.
With three races in Germany's Garmisch-Partenkirchen from Friday - two of them in the super-G for which she holds the world title - and 100 points on offer for each win - Maze looks very likely to smash Maier's record.
The Austrian ex-champion, for one, would be glad to see the record fall, saying he is tired of being asked about it.
"I hope Tina manages the 2,000 points because then no-one will talk to me about it any more," Maier, now 40, told Austrian reporters last month.
Six more races before the season ends in Lenzerheide, Switzerland, on March 17 offer Maze yet more chances to hoover up points.
Not that the Slovenian is worrying about making history. "Records are not my goal but if things go on like this anything's possible," she said earlier in a season that has so far produced eight wins and 10 other podium spots on the World Cup.
Spirited and determined, as befits a competitor in a sport where the women reach speeds of more than 125 kph in downhill races, Maze has always been her own person.
When she fell out with the Slovenian ski team in 2008, she set up her own team - named, almost inevitably, 'aMaze' - with her friend and coach Andrea Massi, following in the ski tracks of strong-minded racers such as Marc Girardelli and Bode Miller who enjoyed success after breaking free from their national federations.
When Swiss rivals accused her of getting aerodynamic advantage from plastic components in her underwear, and the International Ski Federation confiscated her racing bra to investigate, Maze made her thoughts known in the finish area at a race in the Italian resort of Cortina d'Ampezzo.
Unzipping her ski suit, she showed off a white sports bra with the words "Not your business" written across the front in black marker pen as photographers rushed to take pictures.
An accomplished pianist, Maze likes to entertain her fellow racers whenever she finds a piano in the hotels on the five-month tour that makes up the World Cup.
She speaks four languages and opted to sing in English in her catchy song, "My Way is My Decision", which became a hit in Slovenia and on YouTube.
"Every single day is a battle that I know I'm meant to face," Maze sings. "I've got to prove that I'm a winner."
Winning, in the second half of this season, has inevitably been made easier by the absence of American Lindsey Vonn, the overall cup winner four times in the last five years, Olympic downhill champion and double gold medallist from the 2009 worlds.
Vonn took three weeks off over New Year, to deal with health and personal problems and her return was cut short when she broke her leg and tore knee ligaments in the super-G that opened the Schladming world championships at the start of February.
Vonn, though, had her own chance at Maier's points record when she dominated last season but she finished 20 points short.
Maze, who skied her first World Cup race in 1999, a few months before her 16th birthday, hails from the small town of Crna na Koroskem, which has some 2,300 inhabitants, in northern Slovenia.
The town also produced Mitja Kunc, who won a bronze medal in the men's slalom at the 2001 world Alpine ski championships.
Slovenians are extraordinarily proud of their new champion and Prime Minister Janez Jansa, who was voted out on Wednesday, sent Maze a message calling her: "an inspiration to all Slovenians and living proof that all obstacles can be overcome with hard work".
Maze, herself, is well aware that she is living a dream that grew as she watched Croatian Janica Kostelic dominate women's ski racing in the early 2000s.
"When I was younger, I often wondered if I would ever be able to ski like Janica. It was always my wish and now it has come true," Maze told Croatian daily Jutarnji List in January.
"But now I am so good that no one can come close. I feel so good that it is irrelevant who else is skiing against me. My time has come and I hope this fairy tale will last."
- Sports & Recreation
- Hermann Maier