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In the tightest of first sets, there was just one break point on offer for either player, but with Dolgopolov leading 5-4 he was unable to find the point necessary to take the lead. Becker took full advantage in the tie-break by winning the first set with a 7-4 success over the 21st seed in the deciding exchange.
The second set once again proved how evenly matched the two rivals were on the day as another set passed without a break of serve, meaning that Dolgopolov was forced to rely on an emphatic 7-0 success in the tie-break to level the scores.
Dolgopolov grew in confidence to convert the first break point early in the third set, before holding off the challenge from Becker to take a 2-1 lead.
Both players traded breaks midway through the fourth set, but it was a couple of mistakes from Becker in the ninth game which handed the advantage to his Ukrainian opponent.
Dolgopolov was able to wrap up a 6-4 win with a comfortable service game on his way to the third round.