A professional display from the Premier League side against this season's surprise package from League Two saw Nathan Dyer and Jonathan De Guzman net a brace apiece and Michu grab his 19th goal of a memorable campaign as Michael Laudrup's side got their hands on major silverware for the first time in their history and booked a place in the 2013/14 Europa League.
After disposing of Wigan, Arsenal and Aston Villa en route to the final, Bradford arrived in the capital full of hope and cheered on by a partisan travelling support from West Yorkshire.
It did not take long, though, for Swansea's slick passing game to take control of proceedings, with Dyer enjoying early joy down the right flank as the Bantams battled bravely but struggled to gain a foothold in the game.
Ben Davies nodded the first opportunity narrowly wide of the post, as he met an Angel Rangel cross, but the Swans did find the back of the net with just 16 minutes on the clock.
Matt Duke could only parry a low drive from Michu and Dyer was in the right place at the right time to slide the loose ball home at the back post.
Leon Britton fired a half-volley wide from 25 yards as Swansea continued to dominate, before Ki Sung-Yueng was cautioned for clattering through Nahki Wells - who found himself starved of service.
Bradford boss Phil Parkinson would have been looking to get his side into the dressing room with just one goal to chase after the break, but five minutes before the interval Swansea doubled their lead when Michu was allowed to spin inside the box and drill through the legs of Carl McHugh and into the bottom corner.
Things got even worse for the Bantams within two minutes of the re-start, with Dyer able to exchange passes with Wayne Routledge, work the ball onto his left foot and curl past Duke to end the tie as a contest.
A thankless task became an impossible one on 56 minutes, with Duke shown a straight red card for tripping De Guzman as the Holland international skipped past him inside the box.
Dyer pleaded with his colleague to take the resulting spot kick, as he eyed up a cup final hat-trick, but De Guzman refused to relinquish penalty-taking duty and confidently stroked past Bradford's back-up goalkeeper Jon McLaughlin from 12 yards.
Bradford, to their credit, refused to lie down and succumb to a hammering, while their army of loyal followers raised the noise levels inside the national stadium, but the final half-an-hour saw the fourth tier underdogs in damage limitation mode.
Swansea kept passing and probing, posing plenty of questions, and it came as no real surprise when they added a record-breaking fifth in a League Cup final in stoppage-time, with Rangel providing the ammunition for De Guzman to sweep in his second of the game.