The Merseysiders took all three points with an Antony Kay strike in the third added minute when set up by the determined Ian Moore
Tranmere made much of the early running but in them main it was a poor first half with few scoring opportunities.
Richard Taundry blasted wide early on for Walsall who failed to really test Danny Coyne.
The nearest they came was on 27 minutes when a Marco Reich cross hit Andy Taylor and rebounded into the arms of the keeper.
A Moore effort on 13 minutes was beaten out by visiting keeper Clayton Ince, who soon afterwards saved well from a Moore header which followed good work by Gareth Edds.
Kay shaved the outside of a post from 25 yards and then Bas Savage missed the target from a good opening.
The breakthrough for Tranmere came somewhat fortunately on 42 minutes after a corner was played short. A harmless looking Chris Shuker shot from the corner of the box eluded several defenders and was tapped in from close range by a grateful Goodison.
Goodison turned villain on 54 minutes when he tripped Jabo Ibehre deep inside the box. Reich gave Coyne no chance with an excellent strike from the spot.
It was nearly 2-1 on 58 minutes, but Edrissa Sonko saw his shot from Moore's cross rebound off a post. Kay struck the sidenetting with a good effort on 62 minutes and missed the target from the edge of the box late on as Rovers searched for a winner.
Kay had the answer with his fifth of the season to leave Walsall shell-shocked.
Savage and Walsall's Netan Sansara then collected late cautions for over-zealous challenges.
Anthony Gerrard, Rhys Weston and Ibehre took the eye for Walsall. Kay and Steve Jennings worked hard for Rovers.