The 55th-ranked Young trailed 4-1 in the third set before rallying to 4-4. He recovered from 5-3 down in the tiebreaker to win after Monfils' eighth double-fault.
"Lately in the big matches that I've won, I've been down," the 22-year-old Young said. "I just tried to fight and not give up. It paid dividends at the end of match."
The fourth-ranked Murray won 88 percent of points on his first serve in the opening set before stumbling in longer rallies during the second against the 2009 champion. Murray reached 3-0 and 5-2 against Simon in the third but needed six match points to win.
Murray predicted Young will be a tough opponent.
"It's his first final, he's going to be up for it," Murray said. "You never know how a guy will react in his first final ... He might be a bit nervous, but he doesn't have anything to lose."
Monfils' first break point put him ahead 5-4 and he won the first set after a forehand error by Young.
The Frenchman saved one set point while trailing 6-5 in the second before allowing the American back into the match when his own forehand sailed wide and Young clinched the second set.