The visitors gave Vale a 13th-minute present when Lee Hughes was left completely unmarked to claim his fourth goal in four games.
Ryan Burge swung over a far-post free-kick from the left and Hughes buried a downward header from four yards with no Wimbledon players in the frame.
Toby Ajala fired narrowly wide with the best chance for the visitors to equalise, but Vale were firmly in the driving seat when Vincent added a second in the 35th minute.
Wimbledon were penned in their own penalty area and Vincent's left-foot shot from 18 yards took a deflection off a defender, leaving Neil Sullivan stranded as the ball rolled just inside his left-hand post.
The introduction of substitutes Jack Midson and Gavin McCallum briefly lifted Wimbledon with Midson forcing a fine save from Chris Neal on the hour.
But that was a rare foray into Vale territory and the home side were soon inches away from a third when the prolific Tom Pope headed against the crossbar.
Another goal was overdue by the time Vincent chested down a left-wing cross from Jennison Myrie-Williams and drove a 12-yard shot inside Sullivan's left-hand post in the 75th minute.
In the night's other game Oliver Norburn struck in injury time for Bristol Rovers to rescue a point in their clash against Cheltenham in 1-1 draw.
Shaun Harrad's goal in first-half injury time looked to have secured the win for Cheltenham, but a dazzling long-range thunderbolt from Norburn made it four without defeat for John Ward's side.
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- Lee Hughes