Baldock lashed home a shot from the edge of the penalty area in the 93rd minute to cancel out Jermaine Johnson's first-half opener for the visitors and keep alive Sean O'Driscoll's side's slim hopes of escaping relegation.
Johnson struck his first goal since August as Wednesday appeared to have taken another big stride towards safety until Baldock's last-gasp equaliser.
Dave Jones' side had carved out six efforts on goal before Wednesday mustered their first shot, which flew wide from Johnson in the 33rd minute.
City striker Steven Davies' early header was caught by Wednesday goalkeeper Chris Kirkland, who then held on to defender Lewin Nyatanga's curler from the edge of the penalty area.
Davies then saw his angled drive blocked by Owls midfielder Giles Coke before City defender Greg Cunningham fired a shot straight at opposite number Miguel Llera.
City threatened again when Davies headed just wide of the left-hand post with Kirkland stranded midway through the first half, while Baldock's thunderbolt crashed into Wednesday defender Anthony Gardner.
But just two minutes after Johnson had teed himself up with Wednesday's first attempt, the Jamaica international fired the visitors into a 36th-minute lead, guiding home a loose ball in the area into the bottom corner from a central position.
Johnson spurned a golden chance to double the visitors' lead early in the second half when he stabbed the ball wide from six yards.
Johnson later made way for former City favourite Leroy Lita, making his eighth appearance for Wednesday since joining on loan in February, and he pulled a shot from close range wide within a minute of coming on.
Albert Adomah rifled a right-footed shot from inside the area over the crossbar in the closing stages, and, after Owls defender Reda Johnson headed a corner just wide, Nyatanga's stoppage-time shot was blocked by Gardner.
Then, in the 93rd minute, Baldock latched on to the ball on the edge of the area and fired an unstoppable shot into Kirkland's top left-hand corner.