Steve Williams replaced Ramsden in central defence and Michael Flynn led the team out to become City’s eighth different captain this season.
The Bantams enjoyed a let-off when a pinpoint cross by Gary Roberts was headed wide by Pope.
City attempted to hit back but Kevin Ellison volleyed off target and Leon Osborne curled an effort narrowly wide.
Vale continued to shade a tight contest and in the 49th minute Pope rose highest to head Doug Loft’s right-wing corner out of Lenny Pidgeley’s reach and into the net from 14 yards.
Bradford had still failed to place a serious dent in Vale’s rearguard when Pope steered in a low shot after Justin Richards had flicked on a cross by Adam Yates.
Adeyemi slotted an 84th-minute goal after an exchange of passes with substitute Jake Speight, but it proved too little, too late.
Port Vale: Martin, Yates, McCombe, Geohaghon, Collins; Roberts, Griffith, Loft; Haldane (Sutton 86), J Richards (Brown 75), Pope (M Richards 85). Unused substitutes: Tomlinson, O’Shea, K Taylor, Morsy.
Bradford City: Pidgeley, Hunt, Williams, Oliver, O’Brien; Osborne (Speight 70), Adeyemi, Flynn, Ellison; Evans, Dobie. Unused substitutes:McLaughlin, Duff, Dean, Worthington, Lorne, Threlfall.
Referee: Gavin Ward (Surrey).