The 19-year-old netted shortly after his 65th-minute introduction, replacing Jason Koumas, at Prenton Park as Rovers battled back to repeat their New Year's Day draw with Wolves.
Milan Lalkovic gave Walsall hope in the first half that they would achieve their own repeat, having beaten Sheffield United last time out, but it was not to be.
The Saddlers went ahead after 19 minutes in when Lalkovic, on loan from Chelsea, curled a 25-yard strike beyond Tranmere goalkeeper Owain Fon Williams.
Craig Westcarr almost doubled the lead a minute later when he brought a smart one-handed save from Fon Williams. And Ashley Hemmings also forced the home keeper into action from just outside the box as Walsall continued to attack.
Ryan Lowe drew a first save of the game from Richard O'Donnell in the visiting goal as Tranmere came to life after the interval.
Andy Robinson saw a shot fly wide and Everton loanee Matthew Kennedy stung the palms of O'Donnell before Stockton's equaliser.