The Puerto Rican made a slow start to the match, being broken in the opening game but she soon recovered, breaking back to level the score at 2-2 before moving ahead at 5-3 and serving out the set.
She soon skipped into a 5-2 lead in the second but, serving for the match, she lost four straight games and was forced to confirm her victory via a tie-break.
"I'm really excited to be back here in Tianjin and I'm really excited to have won my first match, so I'm really looking forward to continuing and playing some good tennis," she said after the game.
Commenting on the colder conditions in Tiajin, she said: "I just try and warm up my body as much as possible before going out onto the court so I don't feel that cold but you have to deal with it in the end."
The 30-year-old rallied in the second set, claiming it 6-4 but, having fought back from a break down in the decider, her tournament was ended on a tie-break.
Another American to cause an upset was Alison Riske, who overcame fourth seed Timea Babos in three sets. Having cruised through the first set 6-2, the Hungarian was broken late in the second to level proceedings.
Riske raced into a 3-0 lead with two breaks in the decider and though Babos recovered one, the 26-year-old held her nerve to claim a big-name scalp.
Puig, Rogers and Riske will be joined in the second round by Magda Linette, who beat Nina Stojanovic in straight sets, Naomi Osaka knocked out eighth seed Yaroslava Shvedova, 6-4, 6-2, Lara Arruabarrena overcame Fangzhou Liu in three and Evgeniya Rodina triumphed against Christina McHale, 6-1, 5-7, 6-0.