The Valiants almost took an early lead after eight minutes when Jeff Smith swung in a right sided free-kick towards the imposing figure of Akpo Sodje, but his header drifted high and wide.
Rovers threatened the home side's dominance in the 33rd minute when James Coppinger beat Smith allowing him inside the box where he rocketed a right-footed shot that cannoned back off the frame of the goal.
Vale got the goal they deserved two minutes before half-time when a superb turn by Leon Constantine gave the forward room to cross for the arriving Danny Whitaker who applied the finish from five yards out.
Sodje was unlucky not to add to his side's lead soon after the break when he danced his way into a shooting position, but although his shot had the goalkeeper beaten, it failed to find the target.
Whitaker almost had his second of the afternoon after 61 minutes when Danny Sonner's cross caused mayhem in the box, the ball finally dropped for the goalscorer, but his shot was cleared off the line.
Coppinger looked Doncaster's most likely source for a goal but even he found little joy against a staunch defence, eventually hitting a wayward 35-yard effort that flew into the stand behind.
A perfectly weighted through ball by Whitaker gave Constantine his next chance in the 67th minute, but the woodwork yet again denied him with the follow-up also being scuffed by the provider.
Substitute Lewis Guy was given the chance to level the scores a minute later when after going down under little pressure from Goodlad, he was awarded a dubious penalty.
Justice seemed to be done when his casual spot-kick was once again dealt with by the goalkeeper, making a solid stop to keep the lead intact.
The drama didn't finish there when Guy was yet again brought to ground in the area by Richard Walker three minutes from time. Paul Heffernan took a more professional approach and hammered the ball into the back of the net.
The former Bristol City striker wasn't finished there and in stoppage time he grabbed the winner, smashing a shot underneath the unfortunate Goodlad from 12 yards.