Gillesphey gave Bradford an early lead
Macaulay Gillesphey scored in the 13th minute to put the home side in front. Bradford carried that advantage through the remainder of the first half and entered the break one goal ahead.
The opening goal followed a corner from Ciaran Connolly. Gillesphey reached the delivery in the penalty area and gave Bradford a lead after Peterborough’s Mahamadou Khela had sent an early effort wide.
The goal gave Peterborough more than an hour to respond, but the visitors could not find an equaliser before Bradford changed their midfield during the second half.
Phillips scored seven minutes after coming on
Adam Phillips replaced George Lapslie in the 60th minute. Seven minutes later, Phillips scored Bradford’s second goal and increased the lead to 2:0.
Peterborough had entered the round with nine goals in the competition, the joint-highest total before the fourth-round matches. Bradford prevented them from adding to that number at Valley Parade.
Bradford goalkeeper Harry McCracken saved attempts from Edwards and Masara when Peterborough tried to increase the pressure after the interval.
Bradford return to the last eight
Bradford City reached the League Cup final in the 2012/13 season. The club is now back in the quarter-finals, and another win would take Bradford to the semi-finals.
The next opponent will be decided by the quarter-final draw. Bradford did not concede a goal against Peterborough.