After the fourth-round tie between the two sides at the DW Stadium ended goalless after extra time, the visitors won the shootout to progress to the quarter-finals.
© PA Photos
The Latics took the first shot on goal, as Fraser Fyvie tried his luck from outside the area but failed to keep his attempt on target.
Five minutes later, Nahki Wells had a chance to put Bradford in the lead from close range but the forward could not keep his shot on target.
Wells tested Ali Al Habsi with a shot from 30 yards on 44 minutes, but could not get it past the Wigan goalkeeper.
A minute into injury time Gomez forced Matt Duke into making a good save.
Ten minutes after the restart, Bradford midfielder Will Atkinson shot just wide of the Wigan goal.
Soon after Daniel Redmond could not keep his header from a Stam delivery from inside the penalty area on goal.
Midway through the second half Hanson fired a shot from outside the area but failed to keep it on target.
Gomez came close for the Latics with a left-footed attempt from outside the 18-yard box minutes later.
Fyvie tried his luck in the final 10 minutes of normal time and so did Jean Beausejour with a header.
The tie went into extra time and despite both sides creating chances, the deadlock could not be broken and the match went into a penalty shootout.
Bradford prevailed in the shootout as Duke saved Gomez's penalty to win the tie for his side 4-2 on penalties.