Myles Hippolyte put Scunthorpe ahead in the first-half with his first goal for the club, before the hosts levelled through Wes McDonald early in the second half.
After Mark Howard saved a penalty from Josh Gordon, Alex Gilliead struck the decisive goal on 69 minutes, rifling home his first goal of the season.
Cox said: "I'm really proud of the boys. I decided to make a few changes, bringing some fresh legs in and giving a few of the lads an opportunity. I thought those players did really well for me. We all stuck together and showed a lot of fighting spirit, while also playing well.
"We got some good passes in during the first half an hour and got in some good areas. We worked on the formation last week just in case we needed it and felt it was a good time to change a few things.
"In the first half we were excellent and scored a good goal through Myles. In the second half we sat in there, defended and I was proud of the boys' character after we conceded the goal. We were pleased to get the winner through Gilly and win the game.
"Gilly has been excellent. He's played numerous positions for me, he digs in, he cares, is passionate and screams and shouts at people when needed.
"It was great for Myles to score too. He's been telling me he wants to play up front, but we've had other people play there. Tonight I decided to give him the opportunity and he said to me in the dressing room I should keep playing him there.
"His foot was swollen at half-time but he wanted to stay on and play through the pain barrier. We'll see how he is ahead of the weekend. He's a good character and an excellent trainer. He puts a shift in and the fans haven't seen the best of him yet. I'm sure this will give him the confidence to really kick on.
"They (Walsall) thought we were going to play 4-5-1 but we played 4-3-3 and kept the wingers up. We let Dev (Green) run at people and we keep telling him he can be an absolute threat if he believes in himself a little bit more, and that will give him a lot of confidence tonight."
Talking about Howard's penalty save, Cox said: "I have to give Ryan (Simpson) a lot of credit in the analysis room, as the last time we saved a penalty I gave a lot of credit to Mussy (Paul Musselwhite) but Ryan does a fantastic job and doesn't get a mention, so I'm pleased for him tonight."
Ryan Loft was withdrawn at half-time, and Cox added: "Lofty's was after the collision early on, so we will be careful with him and look at him ahead of the weekend."
Aaron Jarvis came on for him but soon had to come off through injury, with Cox saying: "Jarvo looks like he's injured his hamstring so could be a while."
The boss also provided an update on the injury to Emmanuel Onariase sustained at the weekend against Mansfield Town.
He continued: "Manny could be out for a while with a sprained ankle, and that will probably be a month."
See much more from Neil Cox and Myles Hippolyte on iFollow Iron.
