The 15th-seeded 19-year-old from suburban Toronto rallied past 25th seed Mertens 3-6, 6-2, 6-3 to reach a Thursday clash against fellow Slam semi-final debutante Bencic, the Swiss 13th seed who beat Croatian 23rd seed Donna Vekic 7-6 (7/5), 6-3.
"I'm honestly speechless," Andreescu said. "I need someone to pinch me right now. Is this real life?"
Serena Williams, seeking her 24th Grand Slam singles title to match Margaret Court's all-time record, faces Ukraine's fifth-seeded Elina Svitolina in the other semi-final.
Andreescu, a winner this year at Indian Wells and Toronto, is the first teen in the US Open's last four since since Caroline Wozniacki in 2009.
She credited being tested in her wins with giving her the poise to battle back after dropping the first set against a foe who had not dropped a set in the tournament.
"I think it's just the experience from playing these huge events this past year," she said. "All that experience is just catching up."
Andreescu could become the first teen to win a Grand Slam title since Maria Sharapova captured the 2006 US Open and she would be the youngest US Open champion since Russia's Svetlana Kuznetsova in 2004.