Castro's eighth goal of the La Liga season was enough to move Betis - who had Heiko Westermann sent off late on - up to ninth while Les Granotes continue to languish in the relegation zone after Deyverson missed an open goal from seven yards.
Betis made a bright start and were ahead after just four minutes when Castro fired home a right-footed shot.
Joaquin's probing run down the left opened up space in the box and the striker found a gap between Levante keeper Ruben and his left-hand post with precision.
The hosts, though, should have been level just four minutes later when Deyverson somehow failed to score with the goal at his mercy.
The Brazilian followed up on Verza's chipped shot, which hit the post, and somehow saw his effort from close range hit the bar and bounce to safety.
Deyverson then saw an effort narrowly miss the target while Castro almost doubled his side's lead, but for a smart save from Ruben.
Deyverson was having a day to forget and he again hit the bar after the break. This time his 54th-minute shot was sweetly-struck but a left-footed volley from just inside the area failed to dip enough.
Westermann ensured it would be a nervy finish for Betis when he collected a second yellow card 11 minutes from time but the visitors held on.