The visitors showed their attacking intent from the first whistle and forced four corners before taking an 11th minute lead.
Matt Oakley's right-wing cross dropped between Vale's central defenders and Jamie Cureton clipped a close range shot past Chris Neal from eight yards.
It was the 37-year-old's 19th goal of another fruitful season and it was no surprise when the visitors' swift counter-attacks led to a second goal in the 33rd minute.
Vale keeper Neal made a brilliant save to keep out Scot Bennett's shot but he could do nothing as Danny Coles bundled in the rebound from two yards.
Oakley delivered the free-kick which led to the goal and the ex-Southampton star was at the hub of Exeter's three-man central midfield which ran the first-half.
Vale boss Micky Adams brought on Louis Dodds and Rob Taylor at the start of the second-half and it wasn't long before Lee Hughes joined them.
But Exeter were largely untroubled before soaking up the pressure after Mark Molesley was sent off following an off the ball incident 13 minutes from time.
Dodds fired an effort against a post three minutes from time and that was the closest off-colour Vale came to a consolation goal.