The most significant moment of a poor first half was Bira Dembele's raised elbow towards Vale striker Tom Pope, which brought a yellow card for the home defender.
Stevenage thought they had taken the lead in first-half injury time when Francois Zoko headed in Dembele's knockdown from Jimmy Smith's cross, but the Ivorian striker was ruled offside.
Within three minutes of the restart, though, Vale were ahead when Pope nodded home his 12th league goal of the season from a Chris Birchall cross.
Boro responded well as Filipe Morais forced Vale goalkeeper Sam Johnson into a low save and Darius Charles dragged another effort wide.
After 61 minutes Hartley, who replaced Dembele at half-time, headed home Luke Freeman's free-kick to level the scores.
Morais and Freeman went close for Stevenage late on but Graham Westley's men remain in the drop zone after extending their winless run to five games.