The hosts began in the ascendency and were ahead in the 20th minute when highly-rated forward Falcao rolled a challenge before dinking over Gorka Iraizoz from a tight angle.
Falcao gave Atletico a two-goal lead at the break when he converted Diego Godin's looped cross with a flying finish.
The Colombian completed his hat-trick just before the hour mark by converting a penalty after Carlos Gurpegi handled in the area.
He then came close to a fourth goal moments later but his close-range header was kept out by Iraizoz.
The home side made it four six minutes from time when Falcao's replacement Tiago rifled home from outside the area.
Atletico rise to fourth in the table, while Bilbao now prop up the other 19 La Liga teams at the bottom.