Tomer Hemed and Michael Pereira were denied by Betis keeper Espinosa Casto early on before Castro curled in a wonderful free-kick on 23 minutes.
Victor Casadesus came within inches of extending the lead before referee Carlos Velasco Carballo took centre stage in the second period by brandishing three red cards.
Mario was first to go for the visitors before Mallorca duo Ivan Ramis and Victor followed suit for two bookable offences, but even with the extra man for the final few minutes Betis rarely threatened to find an equaliser.
The unusually inclement weather in the Balearics had dominated the build-up to the match as snow had to be cleared from the pitch before kick-off, but it was the hosts who warmed to the task in a largely forgettable encounter.
Hemed's effort on the stretch at the near post nearly embarrassed Casto after only five minutes, but the keeper got enough on the ball to stop it going over the line and collect at the second attempt.
Then the lively Pereira tested the keeper more thoroughly with a fierce drive that he turned round the post.
Mario was somewhat fortunate only to see a yellow card when he pulled down Hemed just outside the box midway through the half, but the free-kick was to prove costly enough for Betis as Castro curled a superb shot in off the inside of Casto's right-hand post.
Victor's speculative volley 10 minutes before the break was the closest the hosts came to doubling their advantage but even once Betis' normal creative lynchpin Benat Extebarria was introduced after half-time the visitors looked devoid of ideas.
Mario did eventually see red on 74 minutes for a late challenge on Tomas Pina which resulted in a second yellow before Ramis suffered a similar fate 10 minutes later when he brought down Ruben Castro.
Victor was also shown a second yellow in stoppage time but Betis' day was summed up when their only shot on target from Salva Sevilla trundled into the arms of Juan Calatayud in the last action of the game.