Betis continued their fine form away from home with a sixth victory in nine games on the road keeping them fifth in the table with an inferior goal difference to Malaga who visit Deportivo La Coruna on Saturday.
Castro fired Betis ahead in the 44th minute at the Romareda when he galloped on to a pass from Nigerian midfielder Nosa Igiebor and finished low past Zaragoza goalkeeper Roberto.
Molina doubled the lead 13 minutes into the second half when he made the most of an error by defender Alvaro Gonzalez before Francisco Montanes pulled a goal back for Zaragoza 13 minutes from time.
Gonzalez's night went from bad to worse when he was shown a straight red card after the final whistle for verbally abusing the referee.
"Away from home we are playing better and starting the year with three points is not a bad thing," Castro, 31, said in an interview with Marca TV.
"There is still a lot of time left in the season and we know it's going to be tough but I think we have a good team, we are doing things well and we'll see if we can keep it up."
Seville-based Betis, who beat champions Real Madrid 1-0 at the end of November, are looking good for a place in Europe next term.
They last took part in European competition in 2005-06 when they finished third in their Champions League group behind Liverpool and Chelsea.
Betis were relegated in 2008-09 before winning promotion back to Spain's top flight two years later.
Unbeaten leaders Barcelona will seek a 17th win in 18 matches when they host city rivals Espanyol on Sunday and may be boosted by the return of coach Tito Vilanova who is recuperating from a throat operation.
Also on Sunday, Atletico Madrid, nine points behind Barca in second, visit Real Mallorca and Real Madrid, a further seven points back in third, are at home to Real Sociedad.
Real Zaragoza had 52.9% of the possession during the loss.
Los Maños had 10 shots, including one on target.
Víctor Rodríguez had three shots for Real Zaragoza, more than any of his team-mates.
The combination of Álvaro González to Abraham was the most common during the match, as the two players connected 17 times.
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