Sevastova was one of Stephens' victims on her run to a first grand slam win at the U.S. Open past year.
In the semifinals, Barty will face the top seed and world No. 1 Simona Halep, the 2016 Rogers Cup victor who defeated sixth-seeded Caroline Garcia 7-5, 6-1 in one hour 28 minutes.
Svitolina rallied briefly to get back to 5-3 but then handed Stephens another break and the first set when she sent a forehand wide.
She broke back for 2-2, but then suffered a letdown as Halep broke service twice more to take the lead.
Simona Halep of Romania hits a shot against Sloane Stephens of the United States (not pictured) during the Rogers Cup tennis tournament at Stade IGA.
Barty took a single break of serve in the first set, before breaking three times in the second and capitalising on her first match point.
Halep had two further chances to claim the victory Stephens' serve, only for the American to produce further impressive resistance to hold. Whenever she has reached the last 4 this season, she managed to win the title. Instead, she played the first evening quarterfinal and now has the early semifinal.
"I've been playing well and it's a good start here to the US Open Series".
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Halep, the 2016 tournament champion, was playing her third match in the past two days after earning two wins on Thursday over Anastasia Pavlyuchenkova and 38-year-old Venus Williams.
"That's a great thing for me".
"I had just over two weeks of no tennis, actually, which is really nice".
"That was kind of the goal for me to keep that consistency, a good level of tennis to cement my spot in the top 20". "I hope in the future it's going to be better".
In the second set, Stevens has drastically added to what Halep was not ready. Obviously, to make a final of another tournament is incredible. "It was really nice for me to go home". "But I know she's very talented".
It was Halep who drew first blood in the decider, but Stephens, looking the fresher of the two, pegged her back at 2-2.
"Both matches were insane good", said Halep.
Stephens and Halep have met eight times so far in a head-to-head the Romanian leads 6-2. "It's maybe the best place because so many people are so nice with me".