Black hit a crucial volley to save the first set point and Murray, who won the mixed doubles at Wimbledon in 2007 with Jelena Jankovic, netted a volley on the second.
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Murray was the only man to lose his serve, in the fifth game of the second, and Paes served out for his eighth Grand Slam title, while Black has now won seven, including three mixed.
"The trick in doubles is to find a good partner," Paes said in a courtside interview. "I let Cara do all the work and just sat back and enjoyed it.