Great Britain had a chance in the fourth set when they earned three breakpoints in the fourth game but Poland won the next five points in a row to take the game and broke Murray in the next game to take a 3-2 lead in the set.
Soderling, who had won six of their previous nine meetings, failed to convert two breakpoints of his own in the next game and the set went to a tie-break.
Ms. Azarenka was both composed and aggressive as she won 12 of the next 13 games, and successfully defended both breakpoints she faced on her own serve in the second set.