The pair performed the same duet routines they wowed the crowd with at last summer's Olympic Games.
At London Randall and Federici finished ninth but they had more to shout about in Italy as they ended the competition in sixth place.
They began with a score of 86.800 for their tech routine and followed that up with 86.740 in their free routine prelim to reach the final.
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The duo then repeated their score in the free routine final to finish on 173.540 – less than four points shy of fourth place.
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USA's Artistic Swimming performance at London 2012