The 68th-ranked Linette held her own in the early going, but Williams gained the only break she needed in the first set in the seventh game and rolled from there.
Two early breaks saw Kanepi up 3-0 in the second before Halep, with the NY crowd behind her, battled back to level the set at 4-4.
"I feel like my game is not at its best, at the best level". "First match of a Grand Slam is always good to get through".
Halep, ranked No. 1 in the world, lost to the unseeded but hard-hitting Kaia Kanepi 6-2, 6-4.
(AAP)Simona Halep and Kaia Kanepi shakes hands after their first round match at the US Open.
Kanepi broke again in the fifth game and never looked back as Halep won just 59 percent of her first-serve points compared to 80 percent for Kanepi in the set. "She played quarter-finals a year ago", she said.
However, she is capable of blasting through opponents and a furious Halep found herself on the wrong end of a 6-2 6-4 scoreline.
It's an experience you can only live in NY and it's one of the best feelings in the world. "I like the atmosphere in the tournament and in the city". "I like the weather: humid and hot". Halep and Serena or Venus Williams were on course. "It's just a chance for them to just hit out".
In addition, defending champions Rafael Nadal and Sloane Stephens were slated to play.
"I didn't play great, but she played really well".
Elsewhere on the opening day, seventh-seeded Spaniard Garbine Muguruza advanced with a 6-3, 6-0 victory over China's Zhang Shuai.
The Romanian known for her fight on court will not forfeit the No. 1 ranking despite her loss, as for the first time since 2016 the WTA's top spot is not on the line during a Grand Slam.