McCann had been selected to cover Burnley's defensive crisis which saw the home side have only three fully-fit defenders.
The 19-year-old, who normally plays a midfield role, surpassed all expectations with a mature performance at centre-half as well as delivering the added bonus of three precious points.
Ipswich dominated the early exchanges and created a couple of chances for former Claret Alan Lee. The first of these arrived after a searching throughball by Gary Roberts, on loan from Accrington Stanley, which saw Lee denied by a fine save from Brian Jensen.
Lee's next opportunity saw him control the ball with his back to goal on the edge of the area and turn sharply before firing wide of the target.
The visitors' 4-1-4-1 formation had proved difficult for the home side to get to grips with and McCann's goalbound volley, which was blocked by a combination of Alex Bruce and Simon Walton, was one of only a few attacking opportunities created by the Clarets.
Town goalkeeper Shane Supple eventually produced his first save to deny Steve Jones after the winger took a pass from Gifton Noel-Williams in his stride and skipped past Bruce.
After a half-time pep talk from boss Steve Cotterill, Burnley started the second half much more brightly with leading goalscorer Andy Gray flicking the ball over keeper Supple, only for centre-half Richard Naylor to head over his own crossbar for a corner.
Gray then combined with Jones only for the winger to see his shot beat Supple and roll inches wide of the far post.
Jones then again eased his way past Bruce but once more Supple proved equal to the test.
It came as no surprise when Bruce was substituted by Sito. Ipswich had rarely threatened in the second period but Jensen had to go full length to push a drive by Walton behind for a corner.
With time running out and the game heading towards a goalless draw, the Town defence switched off for the only time in the game and were left to rue their lack of concentration as McCann fully justified his selection by manager Cotterill by grabbing the winner.