Rebecca Munk Mortensen otherwise got the Danes, who were without Clara Tauson, off to a great start when she defeated Canada's Cadence Brace.
Brace won the first set 6-3, then dropped the next two sets 7-6 (4), 7-6 (4) in a match that took three hours, 41 minutes to play.
Victoria Mboko then brought the tie back on level terms when she defeated Johanne Svendsen 7-5, 6-3 in the best-of-three, Group A playoff match.
“I just wanted to play it point by point and not rush myself, and just believe in myself,” Mboko said during an on-court interview after the win.
Gabriela Dabrowski then teamed up with Mboko to defeat Johanne Svendsen and Emma Kamper Malmkjaer 6-2, 6-4 in 59 minutes to win the best-of-three showdown 2-1.
Canada will play Mexico on Sunday in a winner-take-all showdown, with the winner advancing to the 2026 Qualifiers while Denmark is relegated to the Regional Group 1.