Mirza trailed 3-5 in both sets against the 945th-ranked Nicha before winning in just under two hours.
"She didn't play like she is 945. She hit like she is in the top 50,'' Mirza said. "It's always difficult to play with someone you don't know in the first round. But I'm happy to raise my level and pulled through.''
In other matches, second-seeded Caroline Wozniacki of Denmark shook off a slow start to beat Chan Yung-jan of Taiwan 6-3, 6-0. Yuliya Beygelzimer of Ukraine beat Anastasia Rodionova of Russia 6-2, 6-2 and Neuza Silva of Portugal defeated Jessica More of Australia 6-2, 6-1.
Yaroslava Shedova of Kazakhstan also advanced, beating Tamira Paszek of Austria 6-3, 6-4 and Ivana Lisjak of Croatia stopped qualifier Sesil Karatancheva of Kazakhstan 6-2, 4-6, 6-3.
Mirza reaches 2nd round of Pattaya Open
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