The 18-year-old was taken to hospital in a serious condition
Mirza, who last year finished as runner-up to Vera Zvonareva, made a confident start and broke serve in the opening game.
Malek’s aggressive baseline play allowed her to level at 2-2, but then Mirza took control by dropping just three points in the last four games.
But, instead of solidifying her advantage in the second set, Mirza allowed several opportunities to slip away.
She failed to take a 2-0 lead after holding three break points, and she also failed to convert a fourth break point at 2-1.
Sixth-seeded Mirza finally broke to lead 4-2 when Malek netted a backhand, but instead of riding that advantage to victory she claimed just four of the next 16 points as Malek recovered to level the match.
Three breaks to start the final set left Malek leading 2-1, and although she failed to serve out the match at 5-2, she broke Mirza once more at 5-3 to secure her victory.
Fifth seed Sybille Bammer fared better, but had to battle hard to overcome New Zealand’s Marina Erakovic 7-6 (10-8), 7-5.
The Austrian left-hander broke for 3-2 but was unable to serve out the set at 5-4, and she needed four set points before winning the tiebreak.
Roles were reversed in the second set when Erakovic failed to serve out the set after breaking to lead 5-4, and after Bammer had held serve to lead 6-5 she broke her opponent to claim victory on her third match point.
Third seed Vera Dushevina of Russia had an easier task in overcoming Kazak Galina Voskoboeva 6-4, 6-2, but seventh seed Kimiko Date Krumm of Japan was forced to retire with an left ankle injury when trailing Australia’s Anastasia Rodionova 6-1, 1-0.
The 18-year-old was taken to hospital in a serious condition
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