There are high hopes that Tsitsipas can kick on this year after winning the Next Gen ATP Finals in November and the top seed was too good for Andreozzi, winning 6-3 6-4.
Andreozzi was broken three times and, despite showing character to win three games in a row from 5-1 down in the second set, the lucky loser was unable to take it the distance.
World number 15 Tsitsipas will now come up against Andreas Seppi following the Italian’s 7-6 (7-2) 6-2 triumph over Martin Klizan.
Alex de Minaur, runner-up in his homeland last year, advanced with a 6-4 7-6 (7-5) victory over American qualifier Reilly Opelka, setting up an all-Australian clash with Jordan Thompson.
Third seed Diego Schwartzman coasted to a 6-2 6-3 win over Guillermo Garcia-Lopez, while John Millman took out seventh seed Marton Fucsovics 6-3 6-4.
Yoshihito Nishioka and Gilles Simon progressed at the expense of Andrey Rublev and Sam Querrey respectively.
Fritz claimed the scalp of world number 10 and fellow American Isner, winning 7-6 (7-3) 7-6 (7-5) to reach the quarter-finals in New Zealand.
Top seed Isner served 26 aces, but mini-breaks in each tie-break saw 21-year-old Fritz through.
Fabio Fognini battled his way past Peter Gojowczyk, the third seed from Italy winning 6-2 3-6 7-6 (7-5).
Marco Cecchinato, the third seed, bowed out with a 6-3 6-3 loss to Tennys Sandgren, while Pablo Carreno Busta, Jan-Lennard Struff, Leonardo Mayer, Philipp Kohlschreiber and Cameron Norrie were the other winners on day three.
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