With little between the two sides in the table before kick-off, the hosts took an important lead on 26 minutes through Manny Oyeleke.
Taking their lead into the break, tempers became frayed after the restart before Tom Conlon made it 2-0 just past the hour-mark.
Unable to find a way back into the match Cristian Montano added a third late on to condemn the green and whites to a costly defeat at Vale Park.
In action four days after the visit to league leaders Lincoln City, Darren Way stuck with the same eleven for the midweek trip to Stoke-on-Trent.
Altering shape to the conventional 4-4-2, Tom James reverted to right-back to give Rhys Browne a start in his more natural right wing position whilst Sessi D’Almeida was involved for the first time in a month following a shoulder injury to replace Alex Fisher (ankle) on the bench.
With a settled side the green and whites started on the front foot and had the first shots on goal of the game.
Tristan Abrahams and James both saw efforts fly high and wide whilst at the other end the commanding pair of Omar Sowunmi and Adel Gafaiti stopped the Valiants from registering their first attempt on goal.
Marshalling Vale’s extra man in midfield well to start with, the hosts began to build up a head of steam towards the midway point of the half.
Moving the ball into some threatening positions both Ricky Miller and David Worrall had chances to fire at goal, but Nathan Baxter remained untested as the strikes flew over the bar.
Acting as warnings, the home side continued to fly forward as Town’s boss was forced to match John Askey’s 4-3-3.
However, before the tactical switch had a chance to take effect the deadlock was broken from a corner.
Worrall’s cross flew over the head of James and allowed Oyeleke to power a header into the back of the net as the half-hour mark approached.
Buoyed by the opener the attacking wave continued as Oyeleke almost turned provider by playing in Luke Hannant whose eventual shot lacked any power.
Becoming a half to forget for the visitors they were dealt an injury blow as the break approached, with D’Almeida making his comeback in place of a limping Browne.
Needing the 15-minute break it was almost a 2-0 deficit to come back from when Leon Legge headed wide another Worrall cross, but the score stayed the same at the halfway stage to leave plenty of work to do for Town.
Knowing the damage a defeat could do to any survival hopes a second change was made for the restart as veteran striker Francois Zoko replaced Santos in a switch back to 4-4-2 as Abrahams moved wide.
Taming the Vale onslaught the game became a scrappy affair with a stop-start nature.
With no chances for either side it became a battle in midfield as tempers began to approach boiling point with a number of clashes.
Seemingly frustrating the hosts the final half-an-hour looked to be promising for the green and whites prior to a moment of magic.
The ball fell nicely to Conlon 25 yards out and the midfielder’s first-time dipping strike left Baxter with no chance as it looped into the net.
With only a tame Zoko strike to show for their attacking endeavors the Glovers had Baxter to thank for keeping the score at 2-0.
Working the ball into the box Miller unleashed a venomous strike from the angle that forced the Chelsea loanee to palm away from danger.
Surviving that scare to head into the final 10 minutes, Town then had a chance of their own through substitute Ryan Seager.
Picking up the ball in the box after beating the offside trap the poacher saw his stabbed effort tipped away by Brown to prevent a nailbiting end to the match.
Just about retaining their two-goal advantage the hosts looked to assure their victory and managed it thanks to a substitute.
Montano, introduced moments earlier, was on hand to poke home from close range from Worrall’s wide free-kick to round off the scoring and conifrm a second straight defeat for Way’s side.
Port Vale: Brown; Clark, Legge, Smith, Crookes; Joyce; Worrall, Oyaleke, Conlon (Kay 89′), Hannant (Montano 83′); Miller (Harris 88′).
Bookings: Clark 49′.
Subs not used: Hornby, Howkins, Gibbons, Whitfield.
Yeovil Town: Baxter; James, Sowunmi, Gafaiti, Grant; Browne (D’Almeida 39′), Santos (Zoko 46′), Pattison, Dobre; Duffus (Seager 73′), Abrahams.
Bookings: D’Almeida 55′, Abrahams 63′, Gafaiti 76′.
Subs not used: Nelson, Mugabi, Worthington, Arnold.