McLaughlin turned Evan Horwood’s spot kick onto the underside of the bar to confirm City’s progress after Nathan Doyle, Nahki Wells and Alan Connell had all been successful with their kicks.
Both sides had good chances in a goalless first half with McLaughlin making fine saves to deny Ryan Noble and Charlie Wyke.
The goalkeeper also combined with defender Stephen Darby to force a well-struck Simon Walton effort wide. At the other end, James Hanson was inches away from sliding onto the end of Gary Thompson’s cross from the left.
And Thompson latched onto an Connell pass only to send his shot from the edge of the area over the bar.
City dominated the second half and had enough chances to have settled the tie before the need for a shoot-out. Ritchie Jones was denied by home goalkeeper Scott Flinders 10 minutes after the break and then fired another decent opening over the bar.
Hanson headed a Thompson cross wide and a Wells effort was brilliantly saved as the visitors turned the screw.
They continued to pile forward and went closest to breaking the deadlock with seven minutes remaining when Ricky Ravenhill met a Thompson cross perfectly only to see the ball rebound back off the bar.
That meant penalties and City held their nerve to get through.
Hartlepool United: Flinders; Austin, Baldwin, Hartley, Holden; Franks, Walton (Sweeney 61), Humphreys, Horwood; Noble, Wyke. Unused substitutes: McHugh, Collins, Poole, James.
Bradford City: McLaughlin; Darby, McHugh (Meredith 73), McArdle, Davies; Ravenhill, R Jones (Doyle 68), Atkinson; Connell, Thompson. Hanson (Wells 68). Unused substitutes: Duke, Hines
Referee: G Salisbury (Lancashire).