Rather than looking to score with the stricken keeper in agony, he caught the ball - much to the astonishment of both sets of fans.
The act of sportsmanship earned him praise from around the world, including a letter from FIFA president Sepp Blatter.
The award is made for outstanding contributions to the game, and former West Ham players Ian Wright and Peter Shilton have also received it in the past.
The Carling Awards Panel said: "Paolo Di Canio's actions against Everton were exemplary and showed the true sprit in which this great game should be played.
"As all sports become increasingly competitive, it is refreshing to see a player who hasn't lost the sight of what is still important.
"We believe his actions should be recognised by this very special award."
And Paul says: "Glenn told me about it and I saw the incident on the telly but personally I don't think he could have scored anyway because it was too high!
"It is nice for Paolo, and he gets a little bit of money to donate to charity as well; it is always nice to get awards.
"I remember seeing an interview with Harry straight after the game and he didn't quite know how to react to it.
"He was spitting feathers in one way and saying what a good gesture it was in another.
"Paolo is certainly spontaneous."
MD Paul Aldridge adds: "It was quite a sacrifice by Paolo and we are pleased he has won the award."
Meanwhile, on the transfer front, it has been a frustrating week for Glenn Roeder, who had hoped to bring fresh faces to the club in time for the Sunderland game.
"Glenn has been working very hard to try to make something to happen," says Paul, "and it is at the forefront of Glenn's mind to get something sorted out in a few areas, but it is very difficult.
"The scouting network is out there all the time and Glenn is constantly working at different things."
One short-term signing that has been made this week is the acquisition of Helsingborgs goalkeeper Sven Andersson until the end of the season.
"Sven is a very experienced goalkeeper who has come on a very good recommendation," says Paul.
"He has played Champions' League football for a number of years and we are very confident he will be a sound goalkeeper for us.
"He gives us cover that we certainly need because of Craig Forrest and Steve Bywater being out."