Wozniacki fell to 0-6 in final appearances this season and is 0-3 in head-to-head matches against Svitolina.
The Spaniard had taken the first set before the rain arrived on Friday night, meaning both remaining last-eight showdowns were held over until Saturday morning local time.
Stephens won the last four games and saved three match points to upend Safarova in 2 hours, 11 minutes.
Roger Federer on Saturday raised his game to another level at the ATP Montreal Masters beating Robin Haase 6-3, 7-6 (7/5) to reach the final. "I just kept hanging in there and I thought we both played a really good match". The 27-year-old will bid for her 26th career title on Sunday.
Svitolina will go into the final against Wozniacki with plenty of confidence having a 2-0 career record against her. In the first match, I played well, someone that I don't think I have ever played before...and then second match playing Kvitova is never easy and she's a lefty, which I haven't played in a really long time. Wozniacki leads all WTA players with 46 victories in main-draw matches this season.
Now it will be up to Alexander Zverev to try to dethrone Federer after he outlasted Shapovalov in the day's second semifinal thanks to a pair of key breaks.
She had a straight-sets demolition of 37-year-old Venus Williams and wins over fourth seeded Garbine Muguruza and second seed Simona Halep. It's just tough to play her in these conditions.
"I didn't win, but I think this whole week was a very big personal victory", Stephens said.
On her heels a bit more, Pliskova's unforced errors started to rise.
Halep, who advanced to second on the world ranking, has seemed to lack energy, winning just 43 percent of his first balls-of-service, compared to 84 % for her rival, who also racked up two aces. "I'm just playing better".
Top-seeded Russians Ekaterina Makarova and Elena Vesnina were to meet eighth-seeded Anna-Lena Groenefeld of Germany and Kveta Peschke of the Czech Republic.