Vale, desperate to improve their dismal home form, were soon up against it as the Grecians took a firm grip on the game with goals in the 17th and 19th minutes.
The home defence failed to deal with Matt Gill's left-wing corner for the first, with Berti Cozic striking a post before 35-year-old Marcus Stewart drove home in the scramble that followed.
The visitors' lead was soon doubled with a tremendous individual effort from Liam Sercombe, who ended a driving run with a 20-yard shot that flicked off a defender before looping over a stranded Joe Anyon.
Vale tried hard to get back in the game as skipper Marc Richards snatched a half-chance just wide and David Howland blasted a long range attempt over the top.
Exeter were otherwise largely untroubled as they protected their two-goal cushion until half-time.
Vale provided their first serious threat six minutes after the interval when Ross Davidson's fiercely struck shot drew a smart save to his left by Paul Jones.
The visitors should have wrapped up the points shortly afterwards, however, when Adam Stansfield pulled his shot wide after Stewart's clever header put him in the clear.
Valiants boss Dean Glover brought on striker Luke Rodgers for midfielder David Howland just after the hour in an attempt to turn the screw on the Exeter defence.
But it was all over in the 65th minute when Gill scored direct from a left-wing corner after Anyon allowed the high ball to slip through his fingers in comical fashion.
Ragged Vale did pull one back four minutes from time when Rodgers drove in a close range shot from an assist by fellow substitute Danny Glover.