She won by four shots from American Brittany Lang, who closed with a 67.
It was a second major of the season, and a fifth overall, for the 22-year-old Taiwanese following her 10-shot win in the LPGA Championship last month. She is the youngest woman to win five majors.
Germany's Caroline Masson, the two-shot overnight leader, crumbled to a 78 and finished in a tie for fifth place on nine under par.
Tseng started the final round two shots behind Masson but took the lead by the time she had made her second birdie of the day with a four at the long sixth.
She was four ahead with seven to play and only made a slight stumble with bogeys at the 12th, where she hit her approach through the green, and at the short 13th when she unluckily hit the pin with her tee shot and ricocheted into a terrible spot overhanging a bunker.
But with no one else mounting a charge, she regained control with birdies at the long 14th and 17th and a five-foot putt for birdie at the 18th secured first prize.
"It is a great honour to win the British Open again," said Tseng. "There is so much history attached to this course. I felt more comfortable this year because I learning all the time. My mental game is so much better."
Masson stumbled to the turn in 39 and never looked at ease. But she did birdie the final two holes to rescue a 78 and finished in a tie with the 2009 champion, Scotland's Catriona Matthew (72).
