Monfils qualified for his 19th ATP career final with a 7-6(9) 6-3 win over Ukraine's Alexandr Dolgopolov while Melzer defeated American Sam Querrey 6-2 4-6 6-3.
Both men struggled before wearing down their opponents. Monfils, who was battling pain in his hip, lost the first four games of his match with Dolgopolov and saved three set points to win the opening set tiebreaker.
"It's very good for my confidence. It was good to be down two breaks and to win the set," said Monfils, who is chasing a fifth career title.
Melzer is also chasing a fifth title, and his first since Memphis last year, after surviving a determined fight back from Querrey.