Amauri followed up his goal against Torino on Monday with a brace as Roberto Donadoni's side stretched their unbeaten run to nine games and moved up to seventh in the table.
Second-bottom Livorno, on the other hand, have lost seven of their last eight games and not won for over two months.
Amauri doubled Parma's lead four minutes from time and the striker was on target again from the penalty spot after Emerson fouled Pedro Mendes on a miserable afternoon for Livorno.
In the other Serie A game to be played on Saturday, Davide Ballardini's new side Bologna held his former club Lazio to a goalless draw.
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