Double strikes from Nathan Dyer and Jonathan de Guzman and a goal from Michu was enough to get past the valiant efforts of Bradford who had keeper Matt Duke sent off in the second half.
It was clear that Swansea meant business early on as they dominated possession swiftly moving the ball around and it was the Welsh side that opened the scoring.
After breaking from their own half, Michu received the ball on the left side of the Bradford box which saw his shot palmed by keeper Matt Duke only to see Nathan Dyer race in to slide the rebound home.
The League Two were struggling to create anything at the other end and would have been happy to have gone in at half time only a goal down. But five minutes before half time Swansea doubled their lead with a well taken finish from Michu.
|picture: sky sports|
The tie was all but over minutes after the restart as Swansea added a third through Dyer again. The winger received the ball in the Bradford box and cut in on his left foot, before slotting past the despairing Duke in goal.
With the tie all but over, things went from bad to worse for the League Two side as they were reduced to ten men. Neat play around the Bradford box from Swansea, saw De Guzman receive the ball in the six yard box and after going round the grounded Duke, was cynically tripped by the keeper.
Referee Kevin Friend had little choice but to send the keeper off after denying a clear goalscoring opportunity. As Bradford arranged for their replacement keeper to come on, comedy broke out in the Swansea ranks as De Guzman and two goal Nathan Dyer argued over who was taking the spot kick.
Despite Dyer being on a hat trick, it was De Guzman who stepped up to convert the kick past substitute keeper Jon McLaughlin.
De Guzman added his second and Swansea's fifth late on as he bundled home from close range to leave Swansea celebrating an historic moment in the club's history.
Despite being thrashed, Bradford fans continued to applaud their side after the game, and rightly so as they can look back on a memorable campaign. However focus is now back to the league as they battle for promotion.
Bradford City: Duke, Darby, McHugh, McArdle, Good (Davies 46'), Thompson (Hines 73'), Atkinson, Jones, Doyle, Hanson, Wells (McLaughlin 57')
Swansea City: Tremmel, Williams, Rangel, Davies (Tiendalli 84'), Britton, Michu, Pablo, Dyer (Lamah 77'), Routledge, De Guzman, Ki Sung-Yeung (Monk 62')
Goals: Dyer 16', 47' De Guzman 59' pen, 90' Michu: 40'
Referee: Kevin Friend