The 26-year-old Halep battled through a hard first set, then easily won the second in a rematch of last year's quarter-final contest with Garcia which was also won by the Romanian.
In the deciding set Halep led 5:2, but Stevens refused to admit defeat. Just try to play as well as I can. I feel like she improved in her mental (side) also. I'm playing good tennis.
Halep played four matches in three days after a night session was postponed because of rain.
In the semifinals she will meet reigning US Open champion Sloane Stephens who will contest the second straight semifinal at the Rogers Cup as she easily dismissed Anastasija Sevastova in the last eight 6-2, 6-2.
"My opponent has already six hours at the hotel resting, and I just finished the match and I'm doing now these (interviews)", Halep said at 9 p.m. local time (0100 GMT).
However, with her fourth match point, Halep produced an ace down the middle to settle a gruelling encounter. Then I just went all the way also on her forehand, short, cross, long, everything.
Stephens led throughout the second set, breaking Halep twice, but the Romanian took control of the third set, turning a break into a 5-2 advantage.
With the win Stephens advances to her second consecutive Rogers Cup semifinal after falling to Caroline Wozniacki past year.
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World number 16 Barty reached the semi-finals by reeling off nine of the last 10 games against Bertens.
"Even though I lost today, I literally left everything on the court", Stephens said. "I'll be very late again".
"I had just over two weeks of no tennis, actually, which is really nice".
Stephens broke serve in the opening game and took a 4-0 lead before Svitolina found the range on her groundstrokes. The first year, I think it was 2016, I struggled with injuries, getting my body right, actually being able to go out and play matches.
In a rematch of this year's French Open, World No. 1 Simona Halep and third-ranked Sloane Stephens treated fans to a match with plenty of twists and turns.
"I've been playing well and it's a good start here to the US Open Series".
Halep, who defeated Stephens in three sets at Roland Garros in June, earlier cruised past Australia's Ashleigh Barty 6-4, 6-1 to book her place in the final.