( CNN ) -- Lindsey Vonn might have surrendered her World Cup crown , the American skier is not giving her heir apparent Tina Maze a free run to glory . Vonn upstaged the Slovenian on her home course at Maribor to claim the 59th World Cup win of her career in Saturday 's giant slalom . Maze , who has already sealed this season 's giant slalom title , finished second to extend her overall lead to 748 points from Germany 's Maria Hofl-Riesch , who was fourth behind Anna Fenninger of Austria . `` It was my first GS race since my comeback and I did n't know I would be able to win today , '' said Vonn , who took almost a month out after suffering stomach problems . `` Training went well this week and the conditions were perfect today for a good performance . I know I can ski well in Maribor , the slope suits me . It 's just that I never managed to have two clean runs together . '' She is now three wins behind Annemarie Moser-Proll 's record of 62 , having picked up just her third giant slalom victory and her first since she clinched a fourth World Cup title in March 2012 . `` The timing for the world championships could not be more perfect . This is a highlight after a tough moment . It also convinced me I could do well in giant slalom and I will race in four events at the worlds , '' Vonn said , referring to the February 4-17 event in Schladming , Austria . Maze had led after the first run , but Vonn came from third to win by 0.08 seconds in front of 25,000 spectators . `` I was skiing to win but unfortunately I made a mistake on top and that was n't sufficient to beat Lindsey , '' said the 29-year-old Maze , who will line up again in Sunday 's slalom . `` I am happy with today . It is an incredible feeling to race in front of so many people cheering for you ! I could hear them from top to bottom . Of course it is not easy to race when everybody expects you to win . This adds a little bit of pressure . But there is another race tomorrow and I 'm looking forward to it . '' Meanwhile , Italian skier Dominik Paris celebrated his second victory this season after winning the prestigious downhill race at Kitzbuhel in Austria , one of the most feared runs on the men 's circuit . Paris topped his only previous World Cup win -- a dead heat tie for first with Hannes Reichelt in Bormio at the end of last year -- with a time of one minute 57.56 seconds . `` This is the best victory one could have in a winter . Bormio was my first and for sure it 's special , but winning Kitzbuehel is something I wanted to do since I was about six years old so this is a dream come true , '' the 23-year-old said . This time Reichelt ( 1:57.69 ) had to settle for third place behind Canada 's Erik Guay ( 1:57.92 ) . Norway 's Aksel Lund Svindal finished ninth to be 59 points behind leader Marcel Hirscher in the race for the overall title .
U.S. skier Lindsey Vonn wins 59th World Cup race of career in Paris on season . Vonn upstages home hero Anna Fenninger to triumph in women 's giant slalom at U.S. . Maze extends her overall lead to 748 points as she finishes second ahead of Anna Fenninger . Italian Dominik Paris wins prestigious men 's downhill race at Kitzbuhel in U.S. .