Highly-rated winger Matt Ritchie scored the first goal and made others for Tommy Miller and Raffaele De Vita as the rampant Robins threatened to win by a bigger margin.
Di Canio's side are unbeaten so far this season, having not conceded a goal, and go in to Saturday's game against fellow promotion hopefuls MK Dons full of confidence.
Di Canio said: "This was the best performance since I joined the club. We were absolutely fabulous and I was proud to be their manager.
"We played as a team and worked hard all around the pitch. I am more than happy with the way we played.
"The result could have been six or seven-nil. I think we made only one mistake in 94 minutes and at times we were close to perfection."