They were rewarded for a lively start as they took an early lead through Niall Canavan, and added a further strike through Mark Duffy on 30 minutes.
David Prutton was shown a straight red card towards the end of the opening period for a challenge on James Chambers, but Canavan soon extended the lead after the restart.
Then Leon Clarke added a well-taken fourth with 15 minutes left as Scunthorpe recorded a memorable win in Brian Laws' first league game in charge since his return last week.
The hosts pulled one back at the end through Will Grigg but United held on for the success.
It was their first victory since September 22 when they saw off Colchester United.
The Iron entered the game making four changes from the side beaten by Gillingham on Saturday.
Steve Mildenhall came in for Sam Slocombe to make his debut, while David Mirfin failed a late fitness test on his knee so Canavan came in.
Both back from being cup-tied, David Prutton replaced Michael Collins in the side, while Leon Clarke came in for Mike Grella.
Mildenhall started in goal, with Christian Ribeiro, Paul Reid, Canavan and Tom Newey forming the defence.
The midfield consisted of Mark Duffy, Prutton, Josh Walker and Andy Barcham, while Karl Hawley and Clarke led the attack.
The substitutes were Slocombe, Callum Kennedy, Jimmy Ryan, Damien Mozika, Grella, Connor Jennings and Robbie Gibbons.
The first attack of the game was insitigated by Scunthorpe two minutes in as first Prutton, and then Hawley, had shots on goal blocked away before it eventually went out for a corner - from which nothing came.
Mildenhall was then forced into a quick clearance five minutes later as Jamie Paterson latched on to his poor initial distribution of the ball.
Then, under pressure from Clarke, Walsall shotstopper Grof had to be alert to stop Duffy's right-wing cross, before Hawley then got on the end of a Clarke pass but his effort was deflected wide.
In the 12th minute, Scunthorpe went ahead when Canavan stooped at the back post to head home from a left wing Duffy corner. It was United's first goal from a corner this season.
Just two minutes later, Clarke had a goal disallowed for a push by Hawley in the build-up as he lashed home a stunning volley.
The away side continued to have the better of the opening half and their next chance arrived on 21 minutes when Canavan bulleted a header wide from Duffy's right-wing free-kick.
Four minutes later, former Iron man Andy Butler saved his current side from going two down when he got back quickly to block away a Hawley effort after he was played through down the left side of the home defence by Walker.
On 30 minutes though, they did make it two, as Barcham and Hawley combined down the left side of the penalty area, with the latter teeing up Duffy, who fired home from very close range for his third goal of the season in all competitions.
The first home shot of the match five minutes later, by Jones, was met by ironic applause from the home following as the hosts looked for a way back into the game.
However, there was a blow for the away team in the 44th minute as Prutton was shown a straight red card by referee Tony Harrington after a foul on James Chambers.
Nevertheless, Scunthorpe were undeterred and made it three four minutes into the second half as Canavan glanced home a header from 12 yards after Duffy's left-wing corner found him.
The home side were trying to find a way back into the game but struggled as Scunthorpe blocked and cleared away what was thrown at them.
On 55 minutes, Hawley - now deployed in a holding midfield position in Prutton's absence - clipped an effort over the crossbar after a good driving run from Duffy down the right flank.
Seven minutes later, Mildenhall was drawn into his first save of the game as he made a superb dive to his right to tip away Baxendale's effort, which was dipping into the back of the net.
Two minutes after that, the same player drove an effort wide for the hosts as he drilled a low right-footed effort across Mildenhall, but wide of goal.
The Iron made their first change of the night in the 65th minute when Kennedy replaced Barcham, and the home fans started to become more and more frustrated as their side struggled to create chances and break down the ten men of United.
Scunthorpe soon made it four as, on 75 minutes, Clarke beat the offside trap and latched onto a throughball before rounding Grof and bundling the ball into an empty net.
Mozika replaced Walker with 12 minutes left as he continued his return from a long-term ankle injury lay-off, and he quickly made an impact, crashing into challenges and winning the ball.
The hosts looked for a consolation goal and came close to getting it when Paterson cut inside and fizzed an effort across goal which Mildenhall dived down low to his left to save.
With three minutes left, Ryan replaced Duffy as the away side looked to close the game out.
Just a minute later, Mozika tried to add a fifth as he drove forward before arrowing a left-footed effort towards goal but it was tipped away by Grof.
There were three minutes of stoppage time and Grigg pulled one back at the death for the hosts as he latched on to a loose ball and slotted past Mildenhall.
Scunthorpe are next in action on Saturday when they make the trip to Coventry City.
Walsall: Grof, Taundry, Butler, Holden, Featherstone, J Chambers (Benning, 65), Paterson, Jones (Grigg, 45), Bowerman, Baxendale (Williams, 81), A Chambers.
Substitutes not used: Hemmings, Morris, Downing, Walker.
Scunthorpe United: Mildenhall, Ribeiro, Reid, Canavan, Newey, Duffy (Ryan, 86), Prutton, Walker (Mozika, 78), Barcham (Kennedy, 65), Hawley, Clarke.
Substitutes not used: Slocombe, Grella, Jennings, Gibbons.
Referee: Tony Harrington.
Attendance: 2,787 (126 away).