Most of the first half was instantly forgettable until Davidson was sent for an early bath in the 37th minute.
The teenager went into a rash and high challenge on Karleigh Osborne and referee Andy Haines went straight for his red card.
Vale's fans rounded on Osbourne, who continued after treatment, but the full-back was celebrating when he fired the visitors ahead in the second minute of stoppage time.
Glenn Poole's corner popped up invitingly as several players fought for the ball and Osborne smashed a ten-yard volley, which Joe Anyon could only help into the corner of the net.
Referee Mr Haines was booed from the field by irate Vale fans after sounding the half-time whistle.
No-one would have guessed Vale's ranks had been reduced at the start of the second half as they pressed hard for an equaliser.
But the Brentford defence held firm and as good as put the game to bed with a second goal in the 67th minute.
Again it was a corner from Poole which created the chance and this time Marcus Bean netted an unstoppable header from eight yards.
It could have been three moments later when Dean Bowditch broke clear to strike a shot which Anyon saved to his right.
And Charlie MacDonald went even closer 15 minutes from time when his right-foot snap shot thudded against Anyon's right-hand post.
McDonald finally added a third in stoppage time, belting home his eighth goal of the season after a tremendous run by substitute Adam Newton.