World number five Medvedev, long-touted as one of the most likely of the new generation of players to win a Grand Slam, saw his Rotterdam challenge ended in just 68 minutes by Pospisil.
The 29-year-old Canadian, who continues a fine run of form having reached the final at the Open Sud de France in Montpellier last week, managed to save five of six break points while converting three of his own en route to a huge upset.
Monfils who beat Pospisil in the final to win in Montpellier last week, needed only 70 minutes to dispatch his Portuguese opponent, firing five aces and converting four break points.
The 33-year-old Frenchman, who is looking to become the first player to win back-to-back Rotterdam titles since Sweden's Robin Soderling in 2011, next faces compatriot Gilles Simon who beat Mikhail Kukushkin 7-6(3) 3-6 6-3.
"It's never easy to come back after a win," Monfils said. "But I have great memories from last year."
Carreno Busta fired 11 aces and saved seven break points to advance at his higher-ranked compatriot's expense.
Goffin will face Italian Jannik Sinner, who was awarded a walkover after his opponent Radu Albot withdrew.