The home side asked most of the questions in the first period and were unfortunate not to take an early lead when Koke rattled the crossbar with a strike from outside the box in the 13th minute.
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Just as the two managers were preparing to give their half-time team talks, Antoine Griezmann's deflected strike found its way into the net to give Atletico a one-goal lead at the interval.
Cordoba were level less than 10 minutes into the second half as Ghilas silenced the home fans with a well-placed header, but their parity lasted only four minutes.
Griezmann doubled his tally for the season in the 58th minute with a bullet header from Juanfran's cross which restored his side's slender advantage.
Atletico gave themselves breathing space in the 63rd minute following a Koke free kick, which Mario Mandzukic rose high to meet and get the better of Carlos in the air.
The home side put the result beyond doubt 10 minutes from time when Raul Garcia flicked a header into the top corner from Koke's cross at the end of a move which highlighted why Atletico won the league last season.
Ghilas was Cordoba's standout player, and he capped off an impressive individual display with a consolation goal three minutes from time, capitalising on a defensive lapse from the hosts to reduce the deficit.
The result leaves Atletico just one point behind their table-topping city rivals Real Madrid.