"Today just was not my day", Halep said "The balance was not there".
A long list of returns was scheduled for later today, including past champions Serena Williams, Andy Murray and Stan Wawrinka on the court after missing last year's U.S. Open.
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Romelu Lukaku rounded Hugo Lloris but sent his shot on the angle wide of the open goal from 12 yards. Kane all too easily got free at a corner and directed a super header into the top right-hand corner.
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.
"I have always loved being in NY", said the 33-year-old Kanepi, twice a quarter-finalist at the tournament who has been ranked as high as world number 15.
Kanepi overwhelmed her opponent with her raw power, hitting 26 winners to Halep's nine.
The Estonian got off to a quick start in the match, as she won five of the first six games of the first-ever main-draw match played on the second-largest court at the USTA Billie Jean King National Tennis Center.
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Thomas also added that if their father's heart attack had happened before Meghan was famous she would have rushed to his bedside. Meghan jetted off to Toronto a few days ago for a getaway, but it is highly unlikely that she will visit her estranged family.
Defending champion Sloane Stephens encountered late resistance but held on for a 6-1, 7-5 victory over Russian Evgeniya Rodina. "I like the weather: humid and hot".
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. She struggled throughout Monday's match with Kanepi and coughed up 28 unforced errors. Kanepi, who came within two points of victory before losing their lone encounter at 2014 Doha, was asked what was the secret to her win over Halep, BBC reported.
"She has been playing really well in United States lately, so I thought I just have to be aggressive and try to stay calm". I knew that she can play well here.
"Staying aggressive", Kanepi said, "all the time".
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He also said he would find it challenging not to get information every quarter because so much can change in six months. Nooyi said she thinks it would be beneficial to harmonize American and European rules on financial reporting.