McCann's double - his first was an imperious volley - and a Paul Hayes strike sealed the win for Nigel Adkins' men.
The Blades had drawn level just after the break when Ched Evans fired in a 20-yard free-kick, but it was mostly a poor showing from Kevin Blackwell's men.
Scunthorpe's win was their first Championship victory in five games, while the visitors, tipped for a promotion push this term, have now gone four games without a win and will have to improve considerably if they are to make a bid for the top six.
Both sides took time to settle at the start of the match, and although Gary Hooper was looking lively for Scunthorpe, it was Sheffield United that looked more dangerous.
Stephen Quinn had a vicious volley blocked and after good play down the left, Andrew Davies saw his header cleared off the line.
Just as it looked as if the visitors were going to take control, Scunthorpe stunned them by taking the lead after 22 minutes in the most sublime fashion.
A loose ball fell to McCann and from 30 yards he let fly with a superb dipping volley which beat the helpless Mark Bunn and sailed into the top corner.
Scunthorpe were buoyed by their opening goal and had a glorious opportunity to extend their lead just eight minutes later. A fine flowing move that involved Hooper, Josh Wright and Michael O'Connor ended with McCann feeding Marcus Williams, but the full-back could only blaze his effort over.
The visitors drew level early in the second half.
Scunthorpe defender David Mirfin hauled Evans down when he was through on goal and was lucky to stay on the pitch. However, the hosts did not escape total punishment as Evans drove the resulting free-kick into the bottom corner.
But by the time the 2,000-strong away following had stopped celebrating, they saw their side fall behind again.
After some fine closing down had forced Bunn to put the ball out for a throw-in, Hooper got to the byline and pulled back for Hayes, who poked the ball home from eight yards.
And Scunthorpe were able to forge a two-goal advantage when they scored the third goal in just eight minutes of action.
Hooper was again instrumental as he broke clear and fed Wright, whose measured effort bounced off the upright, but the rebound fell to McCann and the midfielder rifled home his second of the game.
The Blades struggled to respond and never looked like threatening Joe Murphy's goal further.
Scunthorpe were keen to protect what they had and held on for a deserved three points.