He scored in the first half after United were dominant but they were pegged back on the hour mark by Jamal Campbell-Ryce.
The Iron entered the game making one change from the side that drew 2-2 at Shrewsbury a week earlier, as Stephen Dawson replaced Jack King in the starting eleven after being rested.
Luke Daniels started in goal, with Jordan Clarke, David Mirfin, Murray Wallace and Conor Townsend forming the defence.
The midfield consisted of Dawson, Jamie Ness and Neal Bishop, while Jim O'Brien supported Madden and Tom Hopper in attack.
It was Hopper who had the game's first effort, firing wide from 30 yards out which temporarily had Lee scampering across goal. It was a very attacking start from the Iron as they took the game to the Spireites. Dawson got forward but his dummy didn't run kindly for Hopper as he broke through; running out for a goal kick.
After there was some neat play from the Iron as Hopper held the ball up for O'Brien. He played over the top for Madden but it was intercepted.
On seven minutes, Bishop headed over for the Iron from Dawson's cross after good work from Madden.
With ten minutes on the clock, Dawson took a tumble in the area after being fed through the middle. No penalty was given but the attack continued.
Just a minute later, a brilliant ball from Ness set Townsend down the left. His low cross was attacked by Madden, but the defence did well to clear.
On 13 minutes, there was more good attacking play from the Iron involving Clarke on the right. A mis-hit clearance almost found O'Brien, but Lee claimed.
A minute later, Madden steered an effort wide for the Iron from range as the team mounted another attack.
It was one-way traffic and there was another Scunthorpe chance a minute later, as O'Brien took the corner, with Wallace the highest riser in the box. He headed wide of the mark though.
United were rewarded for their endeavour though and took the lead on 20 minutes. Madden got his 20th goal of the season, breaking the offside trap before rounding Tommy Lee and firing low into the net.
Soon after, Bishop sent Madden on his way once more, but good shielding from the home defence saw the ball find Lee.
With 22 minutes on the clock, Lee Novak had the first sight of goal for the visitors, but sent a sliced effort high and wide of the target.
The away side launched an attack five minutes later, when Novak got his knee to a cross from the right which bounced up nicely for Daniels.
In the 32nd minute, the Iron launched the ball forward through Daniels. Hopper flicked on and almost found Madden, but the defence cleared well.
With three minutes of the first half left, Daniels was drawn into his first save of the afternoon, as he was forced to tip over Conor Dimaio's volley from the edge of the area. It proved the last chance of the opening period.
As the second half began, the Iron came out of the traps quickly with Hopper breaking through. The ball didn't bounce kindly though.
The visiting side began to enjoy a bit of pressure though and started to get themselves back into the match. On 51 minutes, there was good defending from the Iron after a Jay O'Shea free kick, which eventually saw the away side push the ball back to Lee.
With 57 minutes on the clock, O'Shea fired a snapshot wide from the edge of the area for the visitors after the ball sat up for him well.
Within two minutes of coming on, visiting substitute Campbell-Ryce made an immediate impact with his first touch, firing into the roof of the net from close range following a low cross from O'Shea.
Scunthorpe made their first change on 65 minutes, with Kyle Wootton coming on for Hopper. Then, shortly after, Luke Williams came on for Neal Bishop as the two substitutes who made an impact last week looked to combine to similar effect seven days later.
With 77 minutes on the clock, O'Brien fired wide of the mark from 30 yards out after good control and a pass from Williams.
Then, a minute later, there was great play from the Iron - starting with Mirfin before Williams fed Wootton. The cross was just overhit. Moments later, Williams arrowed a shot just wide of the left-hand post from 25 yards.
A final Iron alteration was made on 82 minutes, with Gary McSheffrey coming on to face his former club, replacing Ness. He looked to instigate something two minutes later, doing well with the ball, interchanging with Clarke before firing a cross in. Lee claimed with Wootton attacking though.
There were four minutes of added time but neither side could make the breakthrough. United had a final chance at the death, as Lee parried a cross from Clarke into Wootton's path, but the youngster couldn't get to the ball in time as Lee grabbed, and it ended all square.
Scunthorpe United: Daniels, Clarke, Mirfin, Wallace, Townsend, Dawson, Bishop (Williams, 74), Ness (McSheffrey, 82), O'Brien, Madden, Hopper (Wootton, 65).
Substitutes not used: Anyon, Laird, King, Adelakun.
Chesterfield: Lee, Hird, Liddle, O'Shea, Novak, O'Neil, Dimaio (Campbell-Ryce, 59), Anderson, Banks (Talbot, 89), Ariyibi, John.
Substitutes not used: Chapman, Ebanks-Blake, Raglan, Orrell, Slew.