Hleb set up the first two goals for Jean Beausejour and Obafemi Martins in the fifth-round tie at St Andrew's but was then stretchered off and looks doubtful for next weekend's Carling Cup final against his former club Arsenal.
Full-back David Murphy scored the third goal early in the second period and Birmingham were comfortable winners despite making eight changes.
Martins, on loan from Rubin Kazan for the rest of the season, staked his claim to start against the Gunners with an impressive performance and he showed excellent movement.
Veteran midfielder Lee Bowyer also demonstrated his quality with some trademark runs into the Wednesday box while Keith Fahey also caught the eye in a defensive central role.
Blues needed only five minutes to take the lead through Beausejour's first goal for the club.
Hleb's vision picked out Bowyer's late run and the former England midfielder sent the ball across the danger area towards Beausejour. He was unmarked as he side-footed the ball past Nicky Weaver.
Wednesday tried to retaliate and it needed a fine tackle by Roger Johnson to deny Neil Mellor as he prepared to shoot.
But Birmingham were soon back on the offensive and Weaver parried away a powerful Fahey free-kick.
It was one-way traffic and Weaver blocked a close range effort from Beausejour after good play by Murphy.
It came as no surprise when Martins scored his first goal for City after 17 minutes.
Hleb was again the creator with a pass which Martins was able to take into his stride before firing past the exposed Weaver into the far corner of the net.
O'Connor became the first player to be yellow carded after 22 minutes for chopping down Hleb.
It soon became clear Hleb could not continue and was stretchered off before being replaced by David Bentley.
Birmingham continued to dominate and Johnson was only just off target with a header from a Fahey free-kick.
Owls boss Gary Megson made a defensive change after 27 minutes with Richard Hinds replacing Mark Reynolds.
Cameron Jerome prodded wide from three yards out from a low Bentley cross to the near post after getting in front of Weaver.
In a rare Wednesday attack Murphy made a good block on Michael Morrison's attempt.
Tommy Spur became the second Owls player to be booked after 35 minutes for a foul on Beausejour.
Wednesday enjoyed their best spell of the half and Mellor just failed to make connect with a low cross from Daniel Jones after he had got past Stephen Carr.
But in injury-time Bentley shot just wide after the Owls were caught on the counter-attack.
Megson made two more changes at half-time with Mark Beevers and Liam Palmer replacing Michael Morrison and O'Connor.
Blues boss Alex McLeish replaced Jerome with Kevin Phillips for the second half.
When the action restarted Doyle got his body behind a low 25-yard drive from Palmer, while at the other end Weaver punched away a powerful Bentley effort.
After 53 minutes City went further ahead through Murphy.
Weaver punched away Fahey's corner to the near post under pressure from Bowyer.
But Murphy was first to react and drilled his shot home.
Martins should have made it 4-0 but he shot over the bar from close range from Bentley's low centre.
Roger Johnson was booked for a challenge on Hinds and he was replaced shortly afterwards by Jordon Mutch.
Beevers was yellow carded for hauling down Bowyer but much of the sting had gone out of the game give the control Birmingham were enjoying.
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