Ki Sung-Yueng was a surprise choice to partner Ashley Williams at the heart of the Swans defence, while James Hanson and Nahki Wells led the Bantams attack.
The Welsh side started the brighter and dominated possession early on without creating too many clear-cut chances.
That changed with 16 minutes played as Michu fired goalwards from just inside the area and when keeper Matt Duke could only parry the effort, Nathan Dyer closed in to ram home the loose ball.
Bradford were struggling to find any rhythm at this point and after a quiet period of play, Swansea doubled their lead five minutes before half-time.
This time Swans' leading scorer Michu made no mistake as he collected a Pablo Hernandez pass and beat Duke with a left-foot drive low to the Bantams keeper's right.
In the second minute of the second half the Swans wrapped up the game as Dyer raced forward, took a return pass and turned inside his marker before curling a left-foot shot beyond the stranded Duke.
Duke's afternoon got worse just before the hour mark as he was sent off for bringing down Jonathan De Guzman and the midfielder made no mistake from the penalty spot to make the score 4-0.
Bradford offered little in reply and had only one shot on target all game, that coming eight minutes from time, with the Swans having the final word in stoppage time.
Marauding right-back Angel Rangel crossed from the right and De Guzman arrived right on cue to ram the ball home at the near post.