Eighth seed Lopez edged the first-set tie-break before making the vital break in the ninth game of the second and served out for the match.
She broke the Croatian's serve again in the third game of the second set before wrapping up the match when Kostanic sent a forehand long on the first match point.
The second match of the five-game series takes place in Hyderabad on Thursday.
Federer responded by taking the first game of the second set with ease, sending down his first ace of the match.
Sharapova then broke Wozniacki in the first game of the second set and then again once more before serving out for the match at 5-2.
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Burton served the first ace of the match to make it 15-15 in the second game and held to consolidate the break.
Fly-halves Jonny Wilkinson and Olly Barkley missed the Springboks calamity through injuries, while Vickery serves the second game of a two-match ban against Samoa.
Villa made the game safe with a second goal which followed the best passage of play in the match.
But in the days preceding their second round game against Denmark, disputes over match bonuses stoked the fire of discontent in the Nigeria camp.
The man from Bologna eventually held his serve in the second game of the second set, but he seemed to injure himself in the process and conceded the match after 47 minutes of play.
After Djokovic was broken in the first game of the match, Davydenko served for the first set at 5-4 but the second seed fought back to level.
Australia were outplayed by Sri Lanka in the second of three one-dayers on Friday to lose their seventh straight match in all forms of the game.
But it was Dwayne Smith who was named Man of the Series after taking 3-24 from four overs to go with his match-winning 62 not out in the second game of the series.
He saved three match points, including two in the ninth game of the second set which he eventually won 7-5.
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