The 19-year-old has climbed from 152 in the world at the start of the year to 15, and now has a first grand slam semi-final appearance to her name on her Flushing Meadows main draw debut, after her stirring 3-6 6-2 6-3 victory on Wednesday.
Mertens had dropped only 16 games on her way to the last eight, and looked in control after in the first set, but she was eventually blown away by the powerful Canadian.
Mertens, the 25th seed from Belgium, established an early break which she did not relinquish and clinched the opening set with an ace.
It was a low-key start from Andreescu, usually a fiery and emotional competitor, but she broke early in the second only for Mertens to quickly get back on level terms.
However, the youngster was now finding her range, and her voice, breaking twice more to take the set.
Andreescu was beginning to flag on a humid New York evening, drenched in sweat and taking swigs of water between points.
She needed to shorten the points and her aggressive groundstrokes eventually told on Mertens, who was broken in game eight, and a pounding backhand down the line wrapped up the victory.
“This is honestly so crazy,” said Andreescu. “A year ago I was in the qualifying round, and now with what I have accomplished this year I am speechless.
“I need someone to pinch me right now. Is this real life?
“I think the experience from playing these huge tournaments this past year is just catching up.
“Elise played really, really well so I tried to stay calm. I was getting irritated. I told myself to stay calm and stick to the tactics.”
Andreescu will play Belinda Bencic, the 13th seed, in Thursday night’s second semi-final.
“It’s definitely not going to be easy,” added Andreescu. “She’s an incredible player but hopefully I can play my best tennis.”
Bencic defeated Donna Vekic to reach her first grand slam semi-final.
The 22-year-old from Switzerland, who knocked out defending champion and top seed Naomi Osaka in the fourth round, won 7-6 (5) 6-3 against her close friend and frequent hitting partner.
She said: “I think we are professional enough to be friends off the court but do our work on the court and stay focused. I’m sure off the court we are still friends.
“I really like the challenge. Some players are maybe afraid of the big courts but for me it is more motivation. I am really enjoying my tennis.”