The third-seeded Simon rallied from a set down to beat Taipei's Yen-Hsun Lu 6-7 (4-7), 7-5, 6-4, while the Finnish Nieminen battled past No. 7 seed Robin Haase of the Netherlands 7-6 (7-5), 7-6 (7-4).
Nieminen lost to Spaniard Guillermo Garcia-Lopez in last year's Bangkok finale.
Matthias Bachinger was also a second-round winner. The German posted a 7-6 (7-5), 6-3 victory over Thai wild card Danai Udomchoke.
The first round wrapped up on Wednesday as well. German Tobias Kamke bested eighth-seeded Spaniard Pablo Andujar 6-0, 6-1, while Japan qualifier Go Soeda outlasted Slovakian Karol Beck 3-6, 7-6 (7-0), 7-6 (7-4).
The 2011 Bangkok titlist will earn $107,000.