A Hull team featuring just one player from Saturday's win at Torquay provided plenty of spirit before Vale eased into round two.
Former Vale goalkeeper Paul Musselwhite was the only City regular on duty and he was soon picking the ball from the net when Brett Angell poached his 200 career goal in the ninth minute.
Angell nodded in his second from underneath the crossbar 12 minutes before the interval before Hull rallied in the second half the deservedly pulled one back through substitute Clayton Donaldson in the 72nd minute.
But the goal merely jolted Vale back into action and skipper Matt Carragher decided the tie with a blistering shot 11 minutes from time