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The seventh seeded Indians played compact tennis to defeat Marcelo Melo and Andre Sa of Brazil 6-4, 6-2 in just over an hour.
In the quarter-finals, they will take on the winners of the second round match that pits the fourth seeded Swiss pair of Roger Federer and Stanislas Wawrinka against the mercurial Russian duo of Dmitry Tursunov and Mikhail Youzhny.
Paes and Bhupathi were in perfect sync and combined well to negate the Brazilians. Breaking Sa early in the third game put them ahead, and the duo subsequently did not relax their grip over the proceedings as they sealed the first set without much ado.
At a time when games tend to go with the serve, squandering break points is a luxury that a pair can hardly afford and Paes and Bhupathi put themselves right in the driver's seat by breaking Melo in the first game of the second set.
Again, in the seventh game, a couple of double-faults by Sa handed the Indians a golden opportunity to take the match away from the Brazilians, and they did just that, courtesy a scorching Bhupathi winner.
Bhupathi then served out for the set and match to complete the formality that put them right on course for an Olympic medal.
Paes was elated with the performance and said the key now is to sustain it.
"It was a good match. We played sharp tennis. We served well and returned well and we just need to repeat it every day," he told reporters.
"We had come out firing in the first match and we gained a lot of confidence today. It is tough to beat a team that plays so confidently," he added.
Asked how he and Bhupathi could manage to put behind their stormy relationship and dish out such quality stuff, Paes replied, "See, both of are professionals and we know what to do. Mahesh has his way, I have mine. You don't need to hang around together all the time. What is more important is how what we do in the court.
"I'm happy that we played like professionals and there was excellent camaraderie. I think it rather helps that we don't live into each other's life. It rather gives us a breather and helps us do well on the court."