The Colombian opened his account for the season with a brilliant individual effort on 19 minutes and had his second just before half-time as he slotted home Diego Godin's fine cross at the back post.
Athletic continued to offer little resistance after the break and Falcao completed his hat-trick from the penalty spot just shy of the hour mark before Tiago rounded things off with a stunning strike from outside the box late on.
Falcao has now scored seven goals in the last three meetings between the sides having also scored a brace in the Europa League final at the end of last season and his power was far too much for an Athletic defence still without the seemingly Bayern Munich-bound Javi Martinez.
The opener was purely the creation of the former Porto striker's own work as he received a throw-in near the byline, turned Carlos Gurpegui and then dinked a lovely finish over Gorka Iraizoz.
Ander Herrera then went close to an equaliser with a curling effort that drifted just over, but that proved to be as good as it got from Athletic and Falcao should have doubled his tally moments later but wastefully headed over from Arda Turan's perfectly weighted cross.
However, Falcao did not have to wait long for his second of the evening as he nipped in at the back post to bury Godin's wonderful cross.
Marcelo Bielsa introduced Iker Muniain and Ibai Gomez at half-time in a bid to offer the visitors more attacking impetus, but the changes failed to have any tangible effect as Atleti continued to dominate.
The third goal arrived on 57 minutes when Gurpegui was somewhat harshly ruled to have deliberately handled and Falcao confidently stepped up to send Iraizoz the wrong way.
The Athletic keeper then did brilliantly to avoid the scoreline becoming even more embarrassing for the visitors as he denied Falcao his fourth from point-blank range and produced a fantastic double save from Adrian and Koke, whilst Mario Suarez also hit the underside of the bar.
However, Iraizoz could do nothing as Tiago sealed a perfect night for Diego Simeone's men with a superb strike from 20 yards with six minutes remaining.