Birdies at 14 and 15, followed by three closing pars were enough to hold off the fast-charging Tseng, who shot a seven-under-par 66 in the final round that included three birdies in the last six holes.
Shin's total score of 274, 18-under-par was enough to earn the two-times Women's British Open winner her 11th PGA Tour victory.
She said: "I finally won in Australia. I love meat pies and watching kangaroos, I'm so happy. I just focused on my game."
Fifteen-year-old sensation Lydia Ko has to settle for third place after a difficult final round.
Ko went three over par for the first two holes, and though she battled back for a share of the lead with six to play, two more bogeys put paid to her hopes.
The New Zealander, who shot a 10-under-par 63 in the first round, ended up four shots off the pace after a closing 76.
Shin said of her final-round partner Ko: "She's growing up. I think she's taller than me now!
"I really enjoyed playing with Lydia. She missed a few shots today but she's a great player. I really enjoy watching her play."