The Premier League Latics were held to a goalless draw by the lowest-ranked side left in the tournament, with the Bantams winning the shoot-out 4-2.
It was not the only upset of the round, as Championship Middlesbrough moved into the quarter-finals at the expense of local rivals Sunderland at the Stadium of Light.
Scott McDonald was handed a start by Boro boss Tony Mowbray after he scored both of the goals in last weekend's 2-1 Championship win over Bolton from the bench, and the Australian scrambled the ball home from six yards at the near post late in the first half.
It was enough for Middlesbrough to progress as Sunderland lacked the cutting edge that has seen them draw six of their eight Premier League games so far this season.
Southampton were unable to find sanctuary from their Premier League woes, with manager Nigel Adkins' decision to make 11 changes backfiring on him as Leeds secured another top-flight scalp with a 3-0 win.
The Saints have found life tough since leaving the likes of Leeds behind in the Championship in the summer, accruing just four points from a possible 27, and even the bounty of a quarter-final berth could not chivvy them up as goals from Michael Tonge and El-Hadji Diouf, as well as Luciano Becchio's penalty, saw the home side through.
It is not unusual for managers to make changes in this competition - Leeds boss Neil Warnock made four himself - but in view of Southampton's recent struggles, Adkins' choice to rest the entire starting line-up from Sunday's loss to Tottenham, as well as naming an inexperienced bench, looked somewhat strange.
It was not all bad news for Premier League sides though as Aston Villa made the quarters for the third time in four seasons after Christian Benteke scored a late winner against Swindon at the County Ground.
Villa looked to be cruising to victory as goals from Benteke - a £7million summer signing from Genk - and Gabriel Agbonlahor earned them a 2-0 half-time lead.
But the League One side, who had already overcome Stoke in this season's competition, fought back through two goals from substitute Miles Storey before Benteke had the final say.
The one Premier League clash saw Arsenal come from 4-0 down to beat Reading 7-5 after extra-time at the Madejski Stadium.