The number 16 seed won 5-7, 6-4, 6-2, dumping the well-known Maria Sharapova out of the comptition in the process.
It is the second year in a row that Sevastova has made it through to the quarter finals.
"Despite Sharapova taking the driver's seat to start the match, Sevastova's crafty game left the former No. 1 puzzled as the match wore on," said the official website of the US Open, adding that Sevastova played "a near flawless match".
Sevastova now faces Sloane Stephens of the US in the quarter-finals having dropped just one set in the tournament so far.
A few interesting facts about Anastasija and a form guide can be found HERE.
Meanwhile, here's the winning moment.
(Note: it turned out to be a great match against Sloane Stephens, but unfortunately Anastasija lost on the tie break in the third set)