The home side's impressive early play almost earned them the lead when Leon Constantine's excellent close control gave him the chance to shoot but his effort lacked power, never troubling the goalkeeper.
As the visitors eased themselves into the game, Martin Foyle's men went close again with Constantine taking advantage of another Craig James cross, heading inches wide of Willy Gueret's left post in the 31st minute.
The Swan's had a headed chance of their own seven minutes later when Lee Trundle found Owain Tudur-Jones in the centre but the midfielder's glancing header also flew wide of the mark.
The Valiant's took a deserved lead two minutes before the break when Danny Sonner sought out Chris Birchall wide on the right, giving him the chance to supply a pinpoint cross for the arriving Sam Togwell who confidently headed past Gueret.
However, their lead only lasted four minutes with Adebayo Akenfenwa nodding the ball past a helpless Mark Goodlad from close range after Trundle had crept past George Pilkington to supply the cross.
Port Vale never sat back and scored again in the 58th minute with Togwell turning provider when his pass to Michael Cummins allowed the midfielder to strike an unstoppable shot into Gueret's top right corner from 20 yards.
A fired up home team clinched the points soon after with Constantine grabbing his third in two games, heading firmly past the goalkeeper from 10 yards off a Jeff Smith cross.
City put the home fans on the edge of their seats when, after grabbing a late goal through substitute Rory Fallon, Mark McGregor was forced to make a goal line clearance and Trundle rattled the woodwork.