"I'm very happy that I won. I think I played better in the first two rounds," she said after the match. Kanepi, currently world number 44, beat Peterson 6-3 7-6 and is facing Serena Williams next.
"For some reason I was a bit tense, I don't know why. I didn't feel very comfortable. But I managed to concentrate on a few things and just fight," Kanepi said.
With her win, Kanepi makes the US Open's best 16 for the fourth time and the second year in a row. In two of the past tournaments she managed to reach the quarterfinals as well.
Kanepi, who beat world number one Simona Halep in the first round of this year's US Open, also said that while there had been no reason to be nervous playing against the world number one, by now there are expectations, which means that the pressure is increasing as well.
"I won against the world number one, so I should be able to beat all the others as well," she quipped.
Kanepi is the last of the tournament's round of 16 who isn't yet placed for the quarterfinals, facing Serena Williams next. The two have met in four matches, and so far Williams has won all of them in two sets, while Kanepi never managed to win a set against her.
The last time Kanepi faced Williams was in the round of 16 at Flushing Meadows four years ago, when Williams beat Kanepi 6-3 6-3, marking the one time in a grand slam tournament when Kanepi didn't manage to reach the quarterfinals.
Editor: Dario Cavegn