Betis rose to 12th in the table with four points from three games, while Valencia are 19th, having lost three times.
Castro had opened the scoring for Betis in the 38th minute, reaching Cristiano Piccini's pass, composing himself, then slotting the ball past Diego Alves.
Enzo Perez was sent off for diving in violently on Riza Durmisi with his studs up in the 50th minute, before his victim threaded a pass through for winger Joaquin to score in the 54th.
Valencia brought on Munir El Haddadi, on loan from Barcelona, and the impetus he provided helped them recover.
A strike from the forward cracked back off the crossbar as Valencia turned up the heat.
In the 75th minute Dani Parejo set up Rodrigo to score for Valencia before Munir headed on a corner which Antonio Adan parried, only for Ezequiel Garay to fire home for Betis three minutes later.
A late break from Betis allowed Piccini to feed Castro, who scored his second goal and earned the Andalusians three points.
Sporting Gijon continued their fine start to the season, beating Leganes 2-1 to rise to third in the table with seven points from three games.
Nacho Cases opened the scoring before Duje Cop added the second from the penalty spot, with Diego Rico grabbing a consolation goal for the Madrid minnows.
The result helps the Asturian side leapfrog Barcelona, who lost 2-1 against Alaves on Saturday in the weekend's shock.
Athletic Bilbao squeezed past Deportivo la Coruna at the Riazor thanks to a goal from Raul Garcia which gave them their first win of the season.
A stoppage time winner from Sergi Enrich helped Eibar beat Granada away from home.
Pedro Leon put the visitors ahead before Artur Kravets sent Granada level, but Enrich had the final say and sent Eibar sixth with six points from three games.
Real Madrid are top after their 5-2 win over Osasuna on Saturday, their third straight win.
(Writing by Rik Sharma; Editing by Clare Fallon and martyn Herman)
