The American held serve to reach three games all then broke serve in a twelve deuce game after striking a crosscourt on the run forehand passing shot winner.
Williams held her following service game before hitting a forceful crosscourt forehand on set point to score another break of serve and take a one set lead after 51 minutes of play.
The American held serve to start set two after winning her fifth game in a row.
However several forehand unforced errors from Williams combined with improved play from the Pole soon saw the American trailing in set two 1-5.
Williams struck a forehand down the line wide to drop the second set before several additional forehand errors from the American saw her lose her opening service game of set three.
However after dropping serve, Williams reduced her error count and struck an impressive array powerful groundstrokes, volleys and serves to win the final six games of the match.
For the set, Williams produced twelve winners including a surprise ace down the tee on match point to end the contest after two hours and five minutes of play.
In Wednesday’s quarterfinal number one at 11:00 AM Melbourne time (Tuesday at 4:00PM PST USA), Williams meets the 19 year old American Madison Keys who earlier in the tournament upset the 2014 Wimbledon champion Petra Kvitova of the Czech Republic.
In quarterfinal number two, Williams’ sister, the world number one Serena Williams takes on the 11th seeded and 2014 Australian Open finalist Dominika Cibulkova of Slovakia.
Should both sisters win today, they would then face each other in the semifinal round of play.
The Russian and second seed Maria Sharapova is set to face her fellow Russian and the tenth seeded Ekaterina Makarova.
Serena Williams will lose the WTA Tour’s top ranking next week to Sharapova if the Russian finishes with a better result than Williams at Melbourne.