These promotion rivals have now gone five games without a win, but the points looked to be heading the Owls' way after a first half goal from Adam Proudlock.
However Peacock's classic header from a thoughtful left sided cross from Craig Woodman changed all that.
Both sides injected pace and effort into the final 20 minutes, but a draw was fair.
Wednesday had won one battle before the start as City manager Danny Wilson changed the formation.
He played three at the back and used skipper Tom Doherty to occupy the no-mans land just in front of them.
It was not a happy change for City, who often looked suspect in the first half, due to the speed of Michael Reddy.
After one or two scares he opened the way for Proudlock to open the scoring in the 24th minute. It was his first goal since his move from Wolves was made permanent and only his second of the season.
It was a simple goal for City to concede but, inspired by it, Wednesday went on to rattle them and Wilson was happy to rely heavily on Matt Hills' powers of recovery to keep them out of further trouble.
Before the goal he had cleared off the line and set up two chances for his leading scorer Peacock.
The striker squandered the first opening by scooping high over from three yards and he was out of luck with his second effort, latching on to a looping ball from the left back and hitting the foot of the post from 25 yards.
At half time the problem for Wilson was to stop his back line's route-one tactics. If their long balls were not exactly playing into Wednesday's hands they were certainly landing on their heads.
Therefore, the former Wednesday manager made changes to his formation in the second half.
This paid off for him after 69 minutes as Peacock atoned for his earlier misses.
The Owls had little left to offer near goal until Lloyd Owusu glanced a header wide from their first corner in the 71st minute. Nine minutes later he sent their only other chance into the grateful arms of keeper Steve Phillips.