Pope scored a hat-trick to eclipse Wilf Kirkham's 86-year club record by a single day, with his achievement coming just hours after the Alchemy Investment Group took Vale out of administration.
Pope struck twice in two minutes to put Vale in charge. After 20 minutes he chested down a long ball from Clayton McDonald and crashed an 18-yard shot low inside Neil Etheridge's right-hand post, and then headed in Ashley Vincent's cross from close range.
Pope was again heavily involved as Vale added a third in the 36th minute. His header from Richard Duffy's cross came off the inside of Etheridge's left-hand post before Ben Williamson ran in the loose ball.
But Pope was not to be denied and put his name in the record books with a 16-yard header after Etheridge had wandered way off his line.
Pope was substituted just two minutes later and Rovers' sixth defeat in seven games was made worse in the last minute when defender Tom Parkes was stretchered off with a leg injury.