The Blades leapfrogged Leeds United to move into second spot, behind Norwich City, with Kieron Freeman and John Fleck also netting in a one-sided contest.
Blades boss Chris Wilder left top scorers Billy Sharp and David McGoldrick on the bench, giving starts to Madine and a debut to Scott Hogan.
The Blades took the lead after just 38 seconds, Mark Duffy's effort bundled home by Freeman.
Enda Stevens almost added a second, after a game of head tennis, but his effort drifted over the crossbar.
But after some poor defending from the visitors, Madine drilled the ball home.
And it was 3-0 for United on 44 minutes, Madine sweeping the ball home after Marvin Johnson's cross was not cleared.
Five minutes after half-time, midfielder John Fleck fired in a fourth goals for the Blades, whole Ollie Norwood and Hogan were denied a fifth by Emiliano Martinez.
The only question seemed to be how many United would score, but surprisingly they failed to add to their four-goal tally.
Madine was excellent, and next created a chance for the over-lapping Johnson, but once again Martinez denied the hosts.
Hogan was denied a debut goal as Martinez tipped his effort over the crossbar.
Reading offered little in attack all afternoon, the closest they came to a goal when Lewis Baker tested Dean Henderson from 20 yards out.
#Wilder was relieved a calculated risk to rest Billy Sharp paid off.
Wilder said: “You have to pick the right team and we felt that was the right team to go with.
“I feared a slow game and a tired game. It was important we had an energetic performance, what with the way they play.
“They are a possession-based team and we had to commit to that threat, so I wanted us to play a little more forward - Gary (Madine) and Scott (Hogan) allowed us to do that.
“The easy call was to keep the same team. I had to make the right call.”
Wilder was also deeply satisfied with the performance of Cardiff loan signing Madine, who was a robust deputy for Sharp and scored twice in the first half. John Fleck then added the fourth shortly after the interval.
The Blades boss said: “Gary’s been first class in terms of his attitude. He’s done nothing wrong, as far as I’m concerned.
“He showed real character wanting to come here and do well for us. He’s added to a real good group of players. I thought his finishing was excellent.
“Getting off to an unbelievable start was great for us. We looked a threat going forward and we had a good shape behind.
“The Championship is ruthless and relentless and we’ve managed to come through a tough week in decent nick.
“If we can nail the home form that would be great, and a statement we’re doing well. It was a good afternoon, which we’ll enjoy.”
Reading, who had gone four matches unbeaten, were always up against it after such conceding so early and rarely threatened to make a game of it.
And they hardly helped their cause with a first-half defensive horror show - most notably when Madine made it 2-0 after 16 minutes.
Reading are outside the relegation zone on goal difference and next play fellow strugglers Rotherham.
Manager Jose Manuel Gomes said: “I’m disappointed. We didn’t get any points and I’m disappointed with the way we played.
“We conceded a goal in the first minute and we gave all the space to Sheffield to play. They were able to take advantage of the small mistakes we made.
“They are very strong and they showed why they are fighting for different targets to us.
“We never gave up. The fourth goal was a lucky goal, but in football this can happen.
“It was a bad result, but this is now part of the past. We must look forward and prepare ourselves to be stronger in the next match. The next match, in my opinion, will be the match of the season.”