The result was a narrow 7-6 (3), 7-5 victory for the Canadian, who became the first woman from her country to reach the final in Flushing Meadows as well as the first player born in the 2000's to play for a major title.
Andreescu took control of the tiebreak early, jumping out to a 5-0 lead and staged a memorable comeback from 5-2 down in the second set to book a date with Serena Williams in Saturday afternoon's final.
Andreescu fights past Bencic, advances to Saturday's final
The first set was a case of Bencic holding all six of her service game with relative ease while Andreescu struggled in several of hers, needing to save multiple break points.
In the fourth game, she fended off two chances, winning the game with a cross court forehand, three more in the sixth, claiming the game with a drop shot and another in the tenth, sealing matters with an ace.
The set would be decided in a tiebreaker, the Canadian jumping out to a 5-0 lead, aided by a double fault fron the Swiss on the opening point. Bencic pulled the deficit back to 5-3, but a pair of forehand errors clinched the set for Andreescu.
Bencic was quick off the mark in the second, breaking when the Canadian sent a forehand long. Andreescu saved another break point in the third game, but a long rally in which she hit into the net gave the Swiss a 4-1 double break lead.
Breaks were then exchanged and Bencic served for the set at 5-2, but a barrage of winners got Andreescu closer. She held to put the pressure back on the 13th seed at 5-4. Amazingly, the set was back on serve after Bencic double faulted on break point.
Andreescu held for her first lead of the set and after three match points on Bencic's serve, she powered a deep forehand that the Swiss could not get back to advance to Saturday's final.
"I've always dreamt of this moment ever since I was a little kid", Andreescu said in her post-match interview. "But I don't think many people thought it would actually become a reality. I just kept believing in myself.
"But I think that moment after match [point won], I was just in shock. At the same time, I fought really hard to get to this point, so I really think I deserve to be in the finals on Saturday."