With Lee Sinnott's side put under siege the opening goal arrived in the 18th minute. Andrew Hughes went on a long run down the left touchline and his deep cross was headed down into the net at the far post by David Prutton for the former Southampton winger's third goal of the season.
Jermaine Beckford was twice denied by a post as Leeds looked to rubber-stamp their superiority with more goals, but Vale strikers Luke Rodgers and David McGoldrick squandered gift-wrapped chances.
Rodgers somehow missed the target from 12 yards when clean through and McGoldrick, in trying to chip goalkeeper Casper Ankergren, lifted his shot high and yards wide.
Vale manager Sinnott made four changes from the side held to a draw by non league Chasetown in the FA Cup and switched the captaincy from George Pilkington to Rodgers.
He challenged his side to show some bottle in the intimidating Elland Road atmosphere, but it was easy to see why Vale were languishing at the wrong end of the table.
Beckford atoned for his earlier misses with a 55th minute goal fashioned with immense skill. Rui Marques played a pass through to the striker, who tricked the defence by rolling the ball behind him before turning and shooting low into the far corner for his 11th goal of the season.
There was anxiety for Leeds when ace marksman Beckford limped off in the 67th minute to be replaced by Tore Andre Flo, but the Norwegian responded by volleying the third goal in the 83rd minute after Tresor Kandol nodded down Hughes' throw-in.