It meant Andy Murray narrowly failed to make it a golden double as he and Laura Robson earned silver.
Murray returned to Centre Court only 45 minutes after beating Roger Federer to win Singles gold, and it looked like he would be celebrating again when the British pair raced through the first set.
But Mirnyi and Azarenka, the women's world number one, hit back to take the second and it was the Belarussians who prevailed in a close match tie-break to win 2-6 6-3 10-8.
The bronze medal was won by the USA's Mike Bryan and Lisa Raymond, who defeated German pair Christopher Kas and Sabine Lisicki 6-3 4-6 10-4.
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