The FDJ rider almost paid the price for making an early move, but he just held on to claim victory on the 207-kilometre stage from Baeza to Albacete.
Australian Matthews (Orica-GreenEDGE) had to settle for second in a sprint finish, with Slovakian Peter Sagan (Cannondale) third.
Frenchman Bouhanni also won stage two of this year's event.
On a day where a sprint finish always seemed likely, Movistar's Alejandro Valverde retained his 15-second race lead ahead of team-mate Nairo Quintana.
There was no movement in the top 10 despite difficult crosswinds, and Valverde will be pleased with his efforts, given the regular splits in the peloton.
Bouhanni, who revealed afterwards that he was thinking of pulling out of the race after getting sunstroke on Friday, acknowledged he took a risk in the last kilometre, but was delighted it paid off.
"Everyone expected crosswinds today and that meant everyone wanted to be at the front," Bouhanni said.
"I stayed with [team-mate] Geoffrey Soupe in the final kilometres, but I was quite a way back down the line coming up the straight.
"I started my sprint from 300 metres out despite the headwind, because I didn't want to get boxed in.
"Usually, that's too far out for me but I had good legs today."
Elia Favilli (Lampre-Merida) and Francisco Javier Aramendia (Caja Rural-Seguros RGA) were involved in the day's breakaway, but they were hauled in with approximately 40km to go.
With the general classification contenders all remaining in touch, an exciting finish was on the cards as several teams prepared their sprinters for late moves.
Tom Boonen (Omega Pharma Quick-Step) loomed large at one point, but Bouhanni was too good, holding off the challenge of Matthews, while further back, Sagan beat John Degenkolb (Giant-Shimano) for third.
The riders will race for 185km from Carboneras de Guadazaon to Aramon Valdelinares in Sunday's ninth stage.