In the first meeting between these two clubs in 23 years, Banks put the Spireites ahead on 20 minutes but it was soon cancelled out five minutes later by Zak Brown.
But Banks grabbed his second of the afternoon after the break, his fourth in three games, and Will Grigg headed in a late third, to secure the points at Aggborough Stadium in front of more than 1,500 noisy travelling Blues fans.
Kidderminster played the last 10 minutes with 10-men after Reiss McNally was sent off for his second bookable offence.
Despite the Harriers’ position in the relegation zone, this was a really tough examination for Town, who had to stand up to the hosts’ big physical threat and spirited underdog style. But they passed the test and it sets-up the next league game against second-placed Barnet in two weeks’ time nicely.
Kidderminster, who have the worst home record in the league and are the lowest scorers, set their stall out early, winning two early free-kicks, which they launched into the box, as well as bombarding Town’s box with long throws, and that was a sign of things to come.
The hosts had started the better side but it was Chesterfield who had the first clear chance of the game. Jamie Grimes pinged a diagonal ball out wide to Liam Mandeville, who hooked it on to Banks, who headed it into the path of Grigg, but goalkeeper Christian Dibble made a good block.
Moments later, the Harriers had their first opportunity after a long ball forward was not fully dealt with, and that led to Ryan Boot making a smart save from lively debutant Ryan McLean.
The Spireites’ passing had been off the mark in the first 15 minutes, kicking the ball out of play a number of times.
But a swift counter, led by Tom Naylor, was finished emphatically by Banks, who fired home into the bottom corner to put the Blues ahead.
However, the lead did not last long. Town had given away far too many free-kicks and they paid the price when a delivery from the bright Sammie Robinson was headed back across goal by McNally and Brown nodded in from close-range on 25 minutes. That was just Kidderminster’s fifth home goal of the season.
Chesterfield’s passing improved as the half went on, and a first-time ball from Miguel Freckleton into Armando Dobra created a chance but his dangerous shot was well blocked.
Ryan Colclough then delivered a deep cross from the left to the back post but Banks’ threatening volley was blocked behind for a corner.
Great play down the right from Mandeville almost put the Blues back ahead but the sliding Dobra narrowly missed out on applying the finish.
The Harriers forced Boot into another save before the break, blocking from McLean at his near post.
Overall, it had been a tough and uncomfortable half for the visitors. They had struggled to cope with Kidderminster’s physicality, given away too many fouls, and been sloppy in possession at times.
Chesterfield started the second-half on the front-foot and had two quick chances, both saved by Dibble, first from Grigg at the near post after good work by Dobra, and then with his legs from Mike Jones.
Not long after, the Spireites had another chance when Mandeville’s free-kick bounced around in the area, it fell to Naylor, but Dibble parried again.
The action continued, but this time it was down the other end, but Boot made a comfortable stop from McNally, who probably should have done better.
The fast-paced start to the second-half was relentless, this time Naylor going down under a challenge from Dibble, but referee David McNamara was unmoved.
Chesterfield retook the lead on 67 minutes after Freckleton got to the byline and crossed low, Grigg hit the post, but Banks was there to pounce for his fourth goal in three games.
The task of getting back into this match was made harder for the home side when McNally was given his marching orders after receiving his second yellow card.
Town had been better after the break, restricting the Harriers to very little, and they added a third goal from another counter-attack. Substitute James Berry surged forward and played in Naylor, who crossed for Grigg to head in his ninth goal of the season to send the away end barmy.
‘The Blues are going up’ sang the travelling army. Let’s hope they are right.
Chesterfield: Boot; Mandeville, Williams, Grimes, Freckleton; Jones, Naylor; Colclough (Berry, 78), Banks (Oldaker, 90), Dobra (Jacobs, 73); Grigg.
Unused subs: Palmer, Curtis.