McCormack, strongly linked with Ipswich on Wednesday, came on at the start of the second half to replace the injured Jay Bothroyd and scored two well-taken goals in extra time to see off plucky Burton.
The Bluebirds opened the scoring in the 17th minute when Peter Whittingham found himself in space on the left and crossed for Bothroyd to score his second goal in as many games with a neat close-range finish.
Their joy was short-lived, though, as an under-hit backpass from Anthony Gerrard allowed Shaun Harrad to steal in and equalise for the League Two side - his sixth goal in his last eight games.
Dave Jones' injury problems continued to mount when he lost Bothroyd and Adam Matthews in quick succession at the start of the second half.
Both sides were struggling to create chances in a tame start to the second half, McCormack coming closest when he found the side netting from 20 yards.
Whittingham was not too far away with a long-range effort after 69 minutes, while at the other end Greg Pearson was unlucky at the near post when his shot was deflected wide.
McCormack had a header ruled out for offside as normal time ticked away, while Michael Chopra spurned two chances and Gabor Gyepes headed just wide as the Bluebirds upped the pressure in the first half of extra time.
The home side finally snatched a second goal in the 107th minute. A good run from Jason Koumas ended with a shot which was only parried by Adam Legzdins, and the ball eventually fell to McCormack who tucked the ball home via the far post.
Burton found themselves 3-1 down shortly afterwards when McCormack found some space on the edge of the box and picked his spot into the bottom corner.
And Chopra completed the scoring with two minutes remaining, slotting home a superb through-ball from Koumas.