Hewitt, playing in this tournament for the first time, was beaten by Pablo Andujar of Spain 6-3, 4-6, 6-3. Seppi fell to Lu Yen-Hsun of Taiwan 7-5, 1-6, 6-4. Lu will next play Andujar, a semi-finalist at this month's Madrid Open.
Carlos Berlocq of Argentina and Robin Haase of the Netherlands also advanced. Haase faces fourth-seeded John Isner of the US in the next round.
Berlocq didn't face a break point in his 6-2, 6-1 victory over compatriot Leonardo Mayer. Haase beat Marinko Matosevic of Australia 6-1, 6-4.
Victor Hanescu of Romania outlasted Albert Ramos of Spain 6-3, 5-7, 6-4. The 2011 runner-up will meet Albert Montanes of Spain.
Results from the third day of the ATP Nice Open tennis tournament (x denotes seed):
First Round:
Sergiy Stakhovsky (UKR) bt Rogerio Dutra Silva (BRA) 6-2, 6-3
Fabio Fognini (ITA x6) bt Marco Cecchinato (ITA) 1-6, 6-1, 6-2