Phillips stole in at the far post in the 93rd minute to head Scott Sinclair's fine cross beyond Wednesday goalkeeper Lee Grant and salvage something from a game they appeared destined to lose.
Lewis Buxton had broken the deadlock for the Owls with his first goal for the club in the 57th minute.
Owls defender Buxton signed a new permanent deal at Hillsborough on Monday following an impressive loan spell from Stoke and celebrated with what looked likely to be the winner.
The right-back forced City goalkeeper Maik Taylor into a fine reflex save and then headed home the rebound to lift most of an 18,409 Hillsborough crowd.
But Phillips pounced for his 12th goal of the season to deny Brian Laws' side their second win in eight league matches, although City have triumphed only twice now in their last eight.
Owls striker Francis Jeffers began a three-game ban, so Leon Clarke made his long-awaited return to the starting line-up following a hamstring injury.
Birmingham manager McLeish, without James McFadden, who injured medial knee ligaments in the midweek win over Derby, made three changes, with Cameron Jerome, Scott Sinclair and Stuart Parnaby back in the side.
The Blues were still awaiting international clearance for aptly-named Honduran Carlos Costly, for whom City have forked out £500,000 to keep on loan until the end of the season.
Wednesday began in sprightly fashion with Clarke and Michael Gray, on loan from Wolves, prominent, but Owls goalkeeper Grant saved superbly to keep out Lee Bowyer's header from Sinclair's 12th-minute cross.
Clarke was wayward with a volley in reply and Jermaine Johnson's low drive was easily held by visiting goalkeeper Taylor.
Taylor then palmed away Darren Potter's 25-yard free-kick, while Grant parried Sinclair's angled shot at the other end.
Jerome showed great pace shortly after the restart to get beyond Owls skipper Richard Wood before cutting inside and curling a shot inches the wrong side of the far post.
City began the second period with purpose, but it was Wednesday who broke the deadlock following a goalmouth scramble in the 57th minute.
Marcus Tudgay's blocked shot fell to Buxton and, although his first effort was brilliantly kept out by Taylor, the former Stoke defender headed the rebound home.
Only a last-ditch tackle by Liam Ridgewell denied Clarke in the penalty area as the Owls built up a head of steam.
Jerome then beat the offside trap but, as he lined up his shot just inside the box, Wednesday centre-half Mark Beevers slid in to challenge.
By first-half standards the game had come to life. James O'Connor and then Tudgay fired in long-range efforts for Wednesday, which were not far off target.
McLeish sent on Sebastian Larsson and Keith Fahey within the space of four minutes midway through the second period for Parnaby and Lee Carsley respectively.
Marcus Bent entered the fray in the 79th minute, with Jerome making way, and Birmingham set about salvaging a point.
Wednesday defended resolutely from front to back but, as the clock ticked down in injury time, Phillips popped up to steal an unlikely point.
Any reproduction, publication or redistribution of this material without the written agreement of 365 Media Group is strictly forbidden.