Striker McCormack swept the ball home from close range at the far post in the 86th minute following a flick-on from substitute Luciano Becchio as Leeds registered back-to-back home wins.
City midfielder Neil Kilkenny made a stunning return to Elland Road by curling home a first-half equaliser against his former club after Adam Clayton had fired Leeds into a third-minute lead.
Keith Millen's side were left to rue what might have been after taking control of the match once Leeds defender Paddy Kisnorbo had been shown a straight red card in the 64th minute for scything down City striker Nicky Maynard in the box.
But Maynard's subsequent spot kick was saved by Leeds goalkeeper Andy Lonergan and the Yorkshire side snatched all three points thanks to McCormack's seventh goal of the season.
Leeds made two changes, with left-back Aidy White back from suspension and midfielder Adam Clayton returning following a calf injury.
City lined up as they had done last week when losing 1-0 to Brighton and were quick to fall behind at Elland Road as Leeds raced into a third-minute lead.
Robert Snodgrass broke free down the right and his cut-back from the by-line was slammed home from 12 yards into the top corner by Clayton, who had burst forward in support.
But the home side's lead lasted only eight minutes. City midfielder Cole Skuse played the ball inside after making headway down the right and Kilkenny kept his composure 25 yards from goal and curled a fine shot into Lonergan's top right-hand corner.
McCormack went close for Leeds when his angled drive was tipped away at full stretch by David James in the 26th minute and the former England goalkeeper made more comfortable saves from Darren O'Dea's header and another shot from Nunez.
But City gave as good as they got as half-time approached. Striker Albert Adomah forced Lonergan to hold his stinging shot and winger Jamal Campbell-Ryce fired inches over after cutting inside from the right.
McCormack and Snodgrass both lifted shots over the crossbar early in the second half, but City soon wrestled the lion's share of possession.
The visitors were rewarded for their pressure in the 64th minute when they were awarded a penalty and Leeds reduced to 10 men.
Maynard wriggled clear in the penalty area and was blatantly hauled down by Kisnorbo, who was shown a straight red card by referee Fred Graham.
Maynard picked himself up to take the spot kick, but Lonergan guessed right and saved low to his left.
City midfielder Marvin Elliott sent a 25-yard shot fizzing wide and then headed straight at Lonergan as the visitors threatened to make their one-man advantage tell.
Elliott was off target with another header as Leeds battled gamely to weather the storm and substitute Becchio helped snatch the points.
The Argentinian headed the ball on in the area and McCormack pounced to deal City a late blow.