Vale suffered their second home defeat in a row as they also failed to score for the third time in four games. Sub Louis Dodds went closest as he hit the post in the dying minutes.
Micky Adams named the same starting eleven that defeated Torquay with striker Lee Hughes well enough to take a place on the bench.
The Valiants got off to another of their slow starts and Exeter looked dangerous forcing a number of corners. So it was no surprise that the visitors took a deserved lead when the prolific veteran Cureton netted on ten minutes.
Vale felt they may have got a penalty soon afterwards as Vincent was barged in the box but the ref turned down the appeals. Then Purse had a header cleared off the line and Loft had a drive on goal.
But Vale’s efforts were in vain as the visitors took advantage of more hesitant defending and doubled their lead through Coles on the half-hour mark despite the best efforts of Chris Neal.
Micky Adams made two changes at half-time with Rob Taylor and Louis Dodds coming on. The new-look home side then threatened through Pope and Myrie-Williams but were unable to reduce the visitors’ lead.
Vale’s last throw of the dice was the introduction of Lee Hughes at the expense of John McCombe on the hour mark.
Vale continued to push forward and Krysiak made a good save from another Pope effort but Vale were still struggling to create any clear-cut chances against impressive opposition.
The visitors were reduced to ten men with ten minutes left as Molelsey was dismissed for violent conduct after a clash with Daniel Jones.
Vale pushed hard against the ten men but failed to find the net as Dodds hit the woodwork with minutes remaining. But that was the home side’s last decent chance as the Valiants suffered another home blip in their efforts to secure promotion.
Vale: Neal, Duffy, McCombe (Hughes), Purse, Jones, Myrie-Williams, Burge, Loft, Vincent (Taylor), Andrew (Dodds), Pope
Subs: Yates, Shuker, Birchall, Morsy