In a tightly fought replay they held off their League Two opponents to book a home tie with Doncaster.
It is four years since the Rovers of Bristol went beyond this round but after a wasteful first half they came so close to forcing extra time when centre-back Steve Elliott headed against the bar from a corner.
For mobility and pattern of play they matched Vale but could not find the accuracy with their final ball to break through.
They can point to another attempt which matched Elliott's header when a low drive from the left by Stuart Campbell was cleared off the line by Clayton Fortune.
On loan from Bristol City, he didn't put a foot wrong in his duel with Junior Agogo.
Rovers rely heavily on their striker but for all his energy he had a poor first 45 minutes.
His touch was adrift but when he tightened up his game after the break Rovers began to prosper.
Vale knew how vital a first goal was going to be and they grabbed it midway through the first half.
They had been pressing around the penalty area when Nathan Lowndes drifted to his right and seized possession. Birchall moved into a central position in anticipation and was ready with his shot when Lowndes turned the ball back in.
As Agogo settled down Rovers then had their most effective spell of the night.
After Campbell's low drive they sensed another chance to equalise when Agogo beat Fortune to a header but it landed on top of the net.