It was the second consecutive year the Romanian French Open champion exited in the U.S. Open first round.
On a hot and humid day, Halep failed to sustain any kind of service rhythm and her usually stout defence proved no match for the powerful Kanepi's bruising groundstrokes and deft drop shots.
"I have always loved being in New York," said the 33-year-old Kanepi, twice a quarter-finalist at the tournament who has been ranked as high as world number 15.
"I like the atmosphere. I like being here. I love the courts and the climate, and I think that the courts suit my game really well."
Kanepi, world number 44, earned the first break when she launched a back-hand lob over Halep's head to jump out to a 2-1 lead and went on to win five of the first six games while winning 80 percent of her first serve points in the set.
Frustration for Halep boiled over in the second game of the second set when she smashed her racket on the court, earning a racket abuse warning from the chair umpire.
Halep recovered and it appeared a comeback was on when she broke Kanepi to love to level the second set at 4-4.
But Kanepi completed the upset when Halep sent a service return long on match point.
"Today I just lost," Halep told reporters.
"I didn't play great, but she played really well. I knew that she can play well here. She played quarter-finals last year," she said.
"I didn't find the balance today. I couldn't play better, so that's it."
It was the sixth time in the Open era that the number one seed has lost in the first round of a Grand Slam tournament and the first at the U.S. Open.
Halep had looked primed for a long run in New York after she won the Rogers Cup this month and narrowly missed out on back-to-back titles after losing to Kiki Bertens in the Cincinnati final. She pulled out of last week's Connecticut Open with an Achilles injury.
The Romanian can take small consolation from the fact she has amassed enough ranking points to remain world number one after the two-week tournament ends.
(Reporting by Rory Carroll; Editing by Andrew Bolton)
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