Two first-half goals helped los Colchoneros go into the second leg of the quarter-final with a healthy cushion and a clean sheet at the Vicente Calderon on Thursday night
Radamel Falcao opened the scoring early on before Filipe Luis doubled the home side's advantage midway through the first 45 minutes, and a fine performance from on-loan goalkeeper Thibaut Courtois ensured that the score remained that way for the rest of the match.
The hosts named a very strong side for what might be their best chance of lifting silverware this season. Star striker Falcao propelled Atletico to a perfect start, too, as Raul Garcia's whipped cross was thumped into the back of the net by the former Porto forward.
On 23 minutes, after a quiet spell at the Vicente Calderon, Filipe Luis sparked the stadium back into life with a powerful finish, punishing the visitors for failing to clear a Mario Suarez free kick.
Courtois, on loan from Chelsea for a second consecutive campaign, was on hand to deny the visitors any sniff of a comeback. On 30 minutes he pulled off a wonderful double-save to deny Betis a route back into the clash.
And, after an impressive first half, the goalkeeper blocked superbly five minutes into the second half from a dangerous Jorge Molina shot inside the penalty area.
Betis enjoyed the better of the possession in the second period but were unable to convert their chances, and los Colchoneros' tight defence deserves acknowledgement for securing the cup win and keeping a clean sheet in the process.
The victor of the two-legged cup clash will face either Sevilla or Zaragoza in the semi-finals, and Diego Simeone's side will be favourites to progress after this result.