Vale created the first opportunity in the fifth minute when Luke Rodgers fizzed his shot wide after clever play by Tobias Mikaelsson, but Yeovil took the lead in their first attack less than a minute later.
Zoltan Stieber fed Andy Kirk down the left edge of the penalty area and the striker's low cross was tucked away by Gary Dempsey from two yards.
The goal shattered Vale's fragile confidence and the visitors attempted to take advantage as Kirk's shot skidded into the arms of Joe Anyon.
But Vale, to their credit, kept plugging away and levelled through a spectacular effort from left-back Adam Eckersley in the 38th minute.
An attempted cross from Paul Edwards was blocked into his path and Eckersley let fly with a 20-yard shot which flew into the net for his first goal in the Football League.
The goal stung Yeovil back into action and skipper Terry Skiverton almost restored their lead when he headed narrowly wide from Stieber's corner two minutes before the break.
They were back in front seven minutes after the interval with Eckersley taking the shine off his goal when he was guilty of a basic error.
His poor pass was seized on by Lloyd Owusu, who sent Kirk clear to comfortably slot his 13th goal of the campaign.
But Vale showed commendable spirit considering their position and equalised for a second time six minutes later.
A right-wing cross from Chris Herd was deflected into the path of Edwards, who placed a neat header inside Steve Mildenhall's left-hand post.
Vale had the best chances to win it after that, most notably when Mikaelsson got in the way of a goalbound shot from team-mate Keith Lowe.