Monfils, hampered by an ankle injury, prevailed 6-4 3-6 7-6(2) in a quarter-final that took two days to complete because of rain.
The ankle started bothering Monfils in the second set, but after a visit by a physio he elected to continue.
Bautista Agut won the set comfortably and the third went to a tiebreak which Monfils led 5-0 before sealing victory with a huge forehand winner after more than two hours.
On the women’s side, Bianca Andreescu beat American Sofia Kenin 6-4 7-6(5) on Saturday to become the first Canadian woman to reach the championship match of the tournament since 1969.
Andreescu, who shot to prominence with her Indian Wells triumph in March, extended her dream run in her home country when she fired a backhand winner on her fifth match point.
Andreescu had to fight plenty of nerves as she struggled to put away Kenin, who won three consecutive games in the second set to level at 5-5.
When Kenin lost the next game she took a medical timeout and left the court to get treatment on what she later said was a groin injury.
Kenin returned to the court and won a lengthy seven-deuce game to set up the tiebreak during which there was little to separate the players until Andreescu ripped the backhand winner to end the match.
The unseeded Canadian has knocked out some big names this week, including Dutch fifth seed Kiki Bertens in the last 16 and Czech third seed Karolina Pliskova in the quarters.
Andreescu, who improved to 3-1 in career meetings with Kenin, will face three-times champion Serena Williams or Czech qualifier Marie Bouzkova in Sunday's final.