Vale announced on Friday that Glover Snr would leave the club after this final game of the season, with John Ward and Paul Ince among those tipped to replace him.
Louis Dodds had already gone close when he lashed Vale in front from 20 yards after 11 minutes.
Luke Medley forced a fine save from Chris Martin, but Glover Jnr should have doubled the lead with a free header which failed to hit the target. But the teenager made amends for his earlier miss in first-half stoppage time.
Abu Ogogo was sent off for saving the 19-year-old's initial shot on the line. Bees' keeper Ran Kadoch then beat out Glover's penalty, but the midfielder followed up to bury the rebound.
James Lawrie had a third ruled out for offside after the break, before Danny Hart thumped in a consolation for the hosts from 25 yards in stoppage time.