Vale's afternoon began brightly when after only two minutes, Leon Constantine was allowed the room to shoot from the edge of the box, but fired wildly over Steve Wilson's crossbar.
However, their good work was undone in the eightth minute when Sam Aiston's hold-up play inside the area gave Daniel Harrison time to steady himself and hit a low drive inside Mark Goodlad's right post.
The Valiants went in search of a quick reply in the 17th minute, but despite beating his marker after a Tony Dinning through ball, Constantine dragged his six-yard shot wide of the mark.
Tranmere soon had a chance of their own three minutes later when Gareth Roberts' free-kick swung in low for Calvin Zola to volley, but a lack of power allowed Goodlad to collect.
The home side continued to push but struggled to find the break they needed with the solid Tranmere defence restricting them to long-range efforts.
Tony Dinning had the best of a bad lot when his 25-yard drive fell inches wide of Wilson's right post in the 30th minute.
Martin Foyle's men were given the perfect opportunity to level the scores two minutes after the break when Constantine received the ball 10 yards out, but the striker scuffed his shot, sending it wide.
Vale's cause wasn't helped when, after making his long awaited return from injury, Lee Matthews only lasted eight minutes after appearing as a substitute to leave his side with only ten men.
Former Stoke City player Chris Greenacre put the final nail in the coffin in the 90th minute when Jason McAteer supplied a cross to the back post where he headed from four yards past a helpless Goodlad.