The Bees quality on the ball caused Vale problems early on and Adam Forshaw squandered an excellent opportunity before the visitors took a 27th-minute lead.
The goal was a cracker from right-back Shaleum Logan, who cut inside Daniel Jones and unleashed an unstoppable left-foot shot from 25 yards which flew into the top corner of Chris Neal's net.
But determined Vale were only behind for five minutes before they equalised through skipper Doug Loft.
Gavin Tomlin did well to get in a cross from the right flank and although, Loft's first effort was blocked by a defender, he smashed in the loose ball from six yards.
Clayton Donaldson almost restored Brentford's advantage early in the second half when his lob from Jake Bidwell's superb pass narrowly missed the target.
And the visitors failed to make the most of a dominant second-half display through a combination of poor finishing and Vale's dogged defending.