Isner claimed a 6-7 (5/7) 7-6 (7/4) 6-3 win over the third-seeded Spaniard in two hours 36 minutes, claiming the only break of the match in the third set.
The win ensures Isner will become the United States' top-ranked player when the new list is announced, overtaking Mardy Fish.
Isner told www.atptour.com: "I certainly wasn't feeling my best at times out there, but I'm fortunate to be able to get through matches because of my serve.
"I'm very lucky to have that on my side. It wasn't pretty, but I found a way to eventually get it done and I'm proud of that."
The final will be Monaco's second straight match against an American opponent after he beat Michael Russell 5-7 6-1 6-4 in the other semi-final.
Monaco said: "It was difficult to get a rhythm. They were tough conditions, but I'm happy to win the match and be in the final."