In the men's tournament, top-seeded Nicolas Amalgro lost to Michael Berrer of Germany 3-6, 7-6 (5), 6-4.
After leading 4-2, Clijsters lost three straight games before winning three in a row to finish the set.
In the second, Clijsters broke Niculescu in the sixth game, but the Romanian broke right back and then both held serve until Niculescu double-faulted to end the match.
Second-seeded Svetlana Kuznetsova of Russia also advanced, beating Arantxa Rus of the Netherlands 6-2, 6-4.
Marcos Baghdatis also reached the second round, beating Arnaud Clement 7-6 (4), 6-3.