The visitors made a promising start with Conor Hourihane and Onismor Bhasera working Vale 'keeper Chris Neal.
But the home side gradually picked up the tempo as Jennison Myrie-Williams blazed off target before the usually clinical Tom Pope shot wide of a gaping net.
The game swung Vale's way big style when Myrie-Williams scored in the 32nd minute and Argyle striker Nick Chadwick was shown a straight red a minute later.
Myrie-Williams cut in from the right flank to fire a left-footed shot from 20 yards which Rene Gilmartin got a hand to but could not keep out of the bottom corner of the net.
And Chadwick was then given his marching orders for striking Vale winger Ashley Vincent in an off-the-ball incident just seconds after the game restarted.
A Vale team featuring six changes from the one beaten by Fleetwood on New Year's Day were still far from convincing either side of half-time.
But victory was all but sealed in the 55th minute when Pope netted his 24th goal of the season with a downward header from six yards after Rob Taylor swung over a cross from the left flank.
Another goal was overdue by the time Ben Williamson prodded home an eight-yard shot from Pope's pass in the 77th minute.
And Williamson returned the compliment six minutes later when Pope drove a convincing right-footed finish inside Gilmartin's right-hand post.