A disappointing match in which neither team managed to find the back of the net was decided by a shoot-out.
And, with Pools missing three of their spot-kicks, the League Two visitors put their name into the hat for the next round of the competition.
Bradford City had the first chance of a slow opening to the game when a lovely cross from Garry Thompson from the left saw the ball whipped across the face of goal – missing the arriving James Hanson by a whisker.
A new-look Pools eleven took a while to really find their stride this evening and it was the visitors who played more fluidly early on.
Pools’ first half-chance on 14 minutes fell to Simon Walton who met the rebound of an Evan Horwood freekick but the midfielder saw his powerful strike blocked out for a corner.
Thompson had another effort for the Bantams when he burst through from the left but his strike went well over Flinders’ bar.
With the half-hour mark approaching, Cooper’s men began to look a little more likely and the best chance of the game fell to new loan signing Charlie Wyke.
The Middlesbrough striker played a neat one-two inside the area with Horwood before curling a lovely effort at goal. Wyke was denied by a strong McLaughlin save but it was a great strike by the big front man who looked strong for Pools this evening.
While the visitors may have started the half on top, Pools finished in the ascendency.
Peter Hartley had a header on goal from a Horwood corner which went wide of the far post, while Ryan Noble pulled a great save out of McLaughlin on the stroke of half time with a goods strike from a tight angle.
But the visitors came out on top again in the second half, with Scott Flinders pulling off an impressive save to deny former Poolie Ritchie Jones from 12 yards out.
And, with Pools really struggling to create anything to really threaten, Bradford were sensing an opportunity.
There was another chance for Jones who cut in from the left, while James Hanson let rip with a powerful strike which went wide of goal.
A strong period of pressure by the Bantams finally ended as Pools upped the tempo and began to threaten the visiting goal.
Sub Antony Sweeney, brought on in place of Walton, saw a brave effort inside the area blocked out, while Jonathan Franks began to offer more down the right wing.
With the pressure on at the right end, Sweeney, who looked bright and seemed to spark the change in tempo for Pools, saw a neat turn and shot blocked out by the defender as he caused problems inside the box.
Bradford though, were not ready to give up on taking this tie and sub Nahki Wells cut in from the left to fire with pace at Flinders but fortunately the Pools keeper reacted quickly to block.
With Pools appealing against a strong challenge on Wyke on the half-way line that went unpunished, Bradford burst forward again to try their luck – this time a Ricky Ravenhill strike beat Flinders only to crash against the crossbar and bounce out of danger.
But with the 90th minute looming, this game seemed destined to be decided by a penalty shoot-out.
Pools did go desperately close in the dying minutes as Ryan Noble cut in to put a lovely ball across the face of goal but it just evaded Wyke arriving at the far post meaning the chance was missed and the game headed to spot kicks.
Thompson (BCFC)- Missed
Austin (Pools) – Scored
Doyle (BCFC) – Scored
Franks (Pools) – Missed
Wells (BCFC) – Scored
Noble (Pools) – Missed
Connell (BCFC) – Scored
Wyke (Pools) – Scored
Davies (BCFC) – Saved
Horwood (Pools) - Missed
Final Score: Pools 0 Bradford City 0 (Pools lose 3-2 on penalties)
Att: 1777 (224 Bradford City)
Pools: Flinders, Austin, Baldwin, Hartley, Holden, Franks, Walton (Sweeney 62), Humphreys, Horwood, Wyke, Noble
Subs Not Used: McHugh, Collins, James, Poole
Bradford City: McLaughlin, Darby, Ravenhill, Davies, Jones (Doyle 69), Hanson (Wells 69), Thompson, Atkinson, McHugh (Meredith 72), Connell, McArdle
Subs Not Used: Duke, Hines