Roared on by the crowd, the 11th-seeded Frenchman saved five match points in the tiebreak before handing his opponent victory with a netted backhand.
Simon has struggled on clay this year, also losing the decisive match when France lost to Argentina in the Davis Cup quarter-finals last weekend.
Bautista Agut, 59th in the world rankings, secured his first win in a Masters series tournament.
Edouard Roger-Vasselin (France) beat Robin Haase (Netherlands) 6-3 6-2 Roberto Bautista (Spain) beat 11-Gilles Simon (France) 6-3 7-6(6) Nikolay Davydenko (Russia) beat Daniel Brands (Germany) 6-3 6-4 Benoit Paire (France) beat Ivan Dodig (Croatia) 6-4 6-4 Jarkko Nieminen (Finland) beat Viktor Troicki (Serbia) 6-1 6-2 Fabio Fognini (Italy) beat 15-Andreas Seppi (Italy) 3-6 6-4 6-4 Milos Raonic (Canada) beat Julien Benneteau (France) 6-1 6-4
- Sports & Recreation