In a relaxed start to the game, Vale created two early opportunities that Christian Hanson and Craig James spurned.
When the tide changed, Chris Llewellyn was first to shoot for Wrexham. He cut inside from the flank and fired onto Jonathan Brain's right post.
This proved insignificant as, in the 21st minute, a brave knockdown by Dennis Lawrence from Darren Ferguson's corner allowed Andy Holt to thump a shot home from ten yards.
The Valiants were saved twice more by the post as Juan Ugarte almost increased the visitors' lead in the 33rd and 40th minutes. But Vale's defence was breached again in the 42nd minute.
An ineffective offside trap allowed Llewellyn through on goal and he coolly fired into Brain's bottom left-hand corner from a tight angle.
The home side came out with more bite in the second half but a decent final ball prevented any comeback.
Youngster Levi Reid came the closest when he struck Ben Foster's punch back at him from 20 yards only for the goalkeeper to recover and tip over.
Ferguson provided a touch of the spectacular in the 68th minute when he bicycle-kicked Carlos Edwards' right-sided cross over the bar.
The addition of Lee Matthews late on improved Vale's attacking options but an inspired Foster proved too much to get past.