Seppi, who defeated Nick Kyrgios in one of the most entertaining games of the Australian Open earlier this year, made light work of qualifier Radu Albot, winning 6-4, 6-4.
He will face 24th seed Gilles Muller in the next round.
Rublev, who produced one of the shocks of the tournament in Melbourne by beating Andy Murray, defeated Florian Mayer 6-1, 6-1 and will be up against 10th seed Tomas Berdych.
Tomic cited a back injury as he withdrew, with his place going to lucky loser Mikhail Youzhny.
Unfortunately the experienced Russian was unable to take his chance as he was beaten 6-4, 6-1 by qualifier Mikhail Kukushkin.
Denis Istomin, who beat Novak DJokovic in Australia, is also out after a 6-4, 7-6(0) loss against Andrey Kuznetsov.
Elsehere talented youngster Borna Coric is through after a hard-fought 7-6(6), 4-6, 6-3 win against Marcel Granollers.
Robin Haase is also through having come from behind to beat Hyeon Chung 3-6, 6-1, 7-6(6).
Read the original article on Eurosport: Seppi, Rublev progress, Tomic withdraws through injury