The visitors had taken the lead with a 20th minute penalty after John McCombe was penalised for a challenge on Bruno Andrade. Joel Grant fired a confident spot kick low inside Chris Neal's right-hand post to give the Vale goalkeeper no chance.
Micky Adams' men were given a lift just before half-time when Wycombe striker Jo Kuffour was sent off for a second yellow card after clattering into Neal.
Neal kept out Joel Grant's spectacular strike with a magnificent save four minutes into the second period before Vale hit top gear. Substitute Ben Williamson was introduced as a third striker and he was on the field for just five minutes when he equalised in the 59th minute.
Pope's astute pass sent him racing clear and Williamson placed a low shot inside Nikki Bull's right-hand post from 14 yards. And Pope rose highest to nod in Ashley Vincent's left-wing cross from six yards in the 66th minute.
Pope then put a majestic header into the top corner from substitute Kingsley James' right-wing cross before Bull spilled a fierce 30-yard shot from Vincent into the net in stoppage time.