It seemed old habits would die hard once more and add to the frustration for Matt Taylor's Saddlers.
They went ahead through Kieran Phillips after just 28 seconds but proceeded to let in yet another goal from a set play as Ash Eastham equalised in the second half.
A fourth League Two game without a win was then on the cards before Wilkinson stepped up and saved the day.
Making a timely return from a hamstring issue, his 95th-minute corker lifts the mood considerably.
Walsall are now up to 19th in the table after doing it the hard way.
Walsall made just the one change from their last league game, the 2-2 draw at Exeter City.
Jack Rose replaced Carl Rushworth – away with the England Under-21s – between the sticks.
The Saddlers also had Wilkinson make a surprise return to the bench after more than a month out.
Salford had one of their Class of '92 backers in town as Gary Neville watched on from the away end. And he barely had time to take his seat before Walsall raced into the lead.
Phillips picked the ball up just inside the visitors' half and could not be stopped.
He quickly surged past several white shirts, got into the box and guided his left-footed shot into the bottom corner.
Not even half a minute had passed. Ammies keeper Tom King and the rest of his team-mates, it is fair to say, were left shell-shocked.
The Saddlers continued to look lively in the moments that followed as well.
They had the lion's share of possession and won a corner, which saw Jack Earing's deep inswinger narrowly miss Manny Monthe's head.
Pressure on Salford, though, then began to ease and worries started to creep in among the home faithful.
Walsall looked slightly unsure as Ash Hunter's long ball found its way past Monthe, who had to be bailed out by defensive partner Rollin Menayese – getting there ahead of Tom Elliott.
Hunter was then the recipient of a late lunge from Saddlers skipper Joss Labadie, who was shown a yellow card.
Having got through that spell, the hosts would enjoy a couple more chances before the break.
A swift counter-attack saw Emmanuel Osadebe find Brendan Kiernan, whose low drive was gathered by King.
Osadebe was in the thick of it again as his ball inside found Labadie.
He poked it onto George Miller, who was thwarted by King, with boss Taylor then receiving a booking from referee Trevor Kettle as he felt Labadie was fouled by Jordan Turnbull inside the area.
Two Walsall greats in Jimmy Walker and Charlie Ntamark took to the pitch at half-time and received a hearty welcome.
The supporters were not far off being treated to a second goal shortly after the restart, too, with Phillips forcing King into a decent stop.
But without that cushion, there was a sense of unease at the Banks's – and understandably so given previous results.
Labadie picked up a knock and after trying to carry on for a bit, he had to be replaced by youngster Sam Perry in midfield.
The Saddlers went close as Osadebe's well-struck free-kick tested King. All things considered, though, they were not doing enough to trouble the Ammies. And, predictably, they were made to pay.
Walsall conceded their ninth goal from a set piece this campaign as Eastham nodded in Hunter's near-post corner, and it seemed the same old trend of dropping points would carry on.
Thankfully, Wilkinson had other ideas.
Having come on as a late substitute, his fantastic finish from just inside the box well into the six added-on minutes sparked wild scenes of celebration.
They made it more difficult than it needed to be, but the Saddlers are, ultimately, back to winning ways.
Walsall (4-2-3-1): Rose; White, Menayese, Monthe, Ward; Labadie (Perry, 69), Earing; Phillips (Shade, 79), Osadebe, Kiernan (Wilkinson, 82); Miller
Subs not used: Jackson (gk), Leak, Sadler, Bates
Goals: Phillips (1), Wilkinson (90+5)
Salford: King; Shephard, Turnbull, Eastham, Ndaba; Lund (Willock, 79), Lowe; Morris (Love, 79), McAleny (N'Mai, 74), Hunter; Elliott
Subs not used: Jeacock (gk), Oteh, Golden, Smith
Goal: Eastham (76)
Attendance: 5,005 (185 Salford fans)
Referee: Trevor Kettle