Top seed Djokovic had to fight back after his game went awry briefly in the opening set on the way to a second-round win over Argentine Juan Monaco 7-5, 6-2.
Second-seed Murray kick-started his run-up to his US Open title defense with a resounding 6-2, 6-3 defeat of Mikhail Youzhny in their second round match. Both players received a bye in the first round.
Murray, the world number two, who was eliminated a week ago in the Montreal third round, made sure that was not repeated at this hardcourt tournament.
He needed just 70 minutes to see off his Russian opponent and move into a match with Julien Benneteau of France.
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