Di Canio worked until midnight on Friday with 200 fans who gave up their evening to ensure the match went ahead.
The Italian ordered pizzas to feed the volunteers and was rewarded with Swindon's fourth successive home win, 2-0 against Shrewsbury in League One.
After a lifeless first half, the hosts scored twice soon after the break with a penalty from Chris Martin and another goal from Andy Williams four minutes later.
Disappointing Shrewsbury offered little as an attacking force but missed a penalty in the 83rd minute after Alan McCormack had fouled Jon Taylor.
"It was emotional to see kids and their dads helping on a cold night and for what they have done I am thankful," said Town boss Di Canio.
"It was incredible what those supporters did for us but it shows the common feeling. They wanted to come to the game and they wanted us to win. The fact that we won is a present to them."
He added: "This was our worst performance since we lost in the FA Cup to Macclesfield.
"At half-time I said to the players you will be at the training ground on Sunday morning at five o'clock, and they improved straight away.
"We have to keep working hard to stay near the top of the table, but to be in third place is no accident."