The England star came off the bench in front of a Tykes' record crowd of 14,293 and slotted three penalties and a drop-goal to turn the tables on the home side in the final quarter of the match.
Indeed, Leeds made the better start, looking more confident and assured on a bitterly cold day and on a hard surface.
They went ahead after only seven minutes when Gordon Ross landed a penalty but their teenage winger Tom Biggs was injured in the build up play and had to leave the field, removing one of their most potent attacking forces.
The visitors were struggling to find any rhythm and their only meaningful attack came from a kick ahead by Tom May but Leeds managed to win the race to touch down.
Leeds were dominating the game but two mistakes in attacking positions gave Newcastle the chance to come back into the game.
The first came when Ross inexplicably decided to try for a drop goal when continuing pressure looked like bearing fruit. He missed and within minutes Leeds conceded a simple kick for Walder.
In the 24th minute sloppy play again led to an attack breaking down and a penalty being conceded, this time Wilkinson was on hand to slot home the kick.
Leeds hit back three minutes later when John Dunbar won a line-out close to the Falcons' line and the pack forced their way over, Mark Regan getting the final touchdown. Ross missed the conversion, which proved expensive as Wilkinson started to dominate the afternoon.
With Newcastle gaining more possession, especially from the lines-out, the England star nudged them further ahead with a penalty.
Despite missing a first-half injury time effort from 52 metres, there was still time left in the half to drop a goal and put his side 12-8 in front at the break.
The second half started with former Newcastle full-back Tim Stimpson failing with an extravagant drop goal from inside his own half. But the game then developed into a rather dour affair with both defences negating the opposition.
Wilkinson eased over a penalty after 51 minutes and even though Leeds put pressure on the visitors' line, they seldom looked likely to break through again.
With seven minutes to go, Ross landed a penalty to ensure a bonus point but in the end the game fizzled out in midfield.
However the bumper crowd went home having seen what they had come for – Wilkinson back in action and his trusty left boot still dominating play.
For Leeds Tykes:Try: ReganPens: Ross 2
For Newcastle Falcons:Pens: Wilkinson 3, WalderDrop: Wilkinson