Yeovil were unlucky not to take an early lead after only nine minutes when Kevin Gall's right sided cross found Chris Cohen arriving only for him to have his close-range shot superbly saved by Mark Goodlad.
Vale had their first look at goal after 13 minutes when Nathan Lowndes' cushioned header set up youngster Sean Doherty just inside the box but his left-footed half-volley flew wide.
Chris Weale was in action in the 24th minute when Tony Dinning picked the ball up and struck a tricky low drive that forced the goalkeeper to push the ball around his right post.
Craig James was proving Vale's most effective player with his long passes from the back dissecting the Yeovil defence, but a lack of fire power meant the Valiants struggled in front of goal.
David Poole threatened nine minutes before the break when he squeezed the ball through a crowded box with a powerful drive resulting in another top drawer save from Goodlad.
Constantine added to his goal tally in the 52nd minute when, after outpacing Adam Lockwood to pick up the ball, evaded the sprawling goalkeeper to calmly slot the ball into the net from 15 yards.
After little activity at either end, Michael Cummins finally took a chance when he fired a 25-yard shot towards goal but the midfielder couldn't find the target.
A thrilling last five minutes saw Goodlad yet again save his side with a stunning save off Nathan Jones and seconds later George Abbey cleared a Lockwood header off the line.
The Glovers almost sneaked a point in stoppage time when Cohen played Phil Jevons through on goal but, luckily for the home side, his effort rolled past the post.