The Seasiders knocked Vale out of the FA Cup and also recorded a league victory at Vale Park, but we made to pay for a string of missed chances in an entertaining first half .
Danny Coid hit the post after just eight minutes and John Murphy saw a header well saved by Jonathan Brain from close range.
Blackpool's best chance fell to lively Scottish striker Keigan Parker, who outpaced the Vale defence but lifted his shot over the bar.
There were chances at the other end and influential midfielder Robin Hulbert came close to scoring a goal of the season contender with a shot from the halfway line which rattled the crossbar with keeper Kevin Stuhr-Ellegaard well beaten.
Vale finally took the lead with just 18 minutes left, when Mathews hit a low free-kick that evaded the wall and Ellegaard to put the visitors in the driving seat.
Blackpool threw on on-loan striker Simon Lynch but fell further behind after Peter Clarke was harshly adjudged to have handled the ball in the area. Mathews stepped up to convert the spot-kick.