PERTH, Australia — Alize Cornet overcame fatigue and French teammate Gilles Simon overcame some rustiness to beat Taiwan at the Hopman Cup on Saturday.

Cornet beat Hsieh Su-wei 6-4, 6-4 and Simon, who moved up in the rankings from No. 29 to 7 last year, defeated Lu Yen-hsun 6-3, 7-6 (8). The two then combined to beat Hsieh and Lu 6-4, 7-6 (9) in mixed doubles to complete France's 3-0 win, saving five set points in the tiebreaker. The duo will play Italy on Tuesday.

The defending champion United States, represented by Meghann Shaughnessy and James Blake, takes on Slovakia on Monday.

The U.S, Australia, Germany and Slovakia are playing in Group A while Russia, France, Italy and Taiwan are in Group B. The winners of each group play in the final next Friday.

Simon had problems closing out the Taiwanese player in the second set, allowing Lu to break his service in the sixth game to get back into the match and force a tiebreaker.

Both Cornet and Hsieh had problems with their serves in the opening set, and Hsieh was 0-for-4 in her breakpoint chances. Cornet succeeded once in five tries — in the ninth game when she took a 5-4 lead — then held serve and won the set with an ace.

It was the only Saturday match at the mixed teams event. On Sunday, Russia, featuring the brother-sister combination of Marat Safin and Dinara Safina, plays Italy's Flavia Pennetta and Simone Bolelli.

Lleyton Hewitt, who hasn't played since the Beijing Olympics due to a hip injury and subsequent surgery, partners Casey Dellacqua when Australia takes on Germany in one of two matches Monday.