Monk had revealed in his pre-match press conference that he is no longer on speaking terms with former assistant Clotet, who took over from Monk as interim head coach at St Andrews when the latter was sacked in June.
Spaniard Clotet had previously worked with Monk at Swansea and Leeds before the duo teamed up again at Birmingham in March 2018 – and the Blues had responded to Monk's comments with a tweet suggesting their former manager lacked class.
The home side started strongly and Barry Bannan fired over from 20 yards with the game's first opening before Steven Fletcher volleyed across the face of Connal Trueman's goal after the ball fell kindly for him in the box.
Jeremie Bela created Birmingham's first chance after 14 minutes but skewed his shot wide after a mazy run.
Fletcher wasted a golden opportunity in the 17th minute when his heavy touch cost him a clear sight of goal after excellent build-up play from Massimo Luongo and Morgan Fox.
Kieran Lee was denied by Trueman after 33 minutes as the hosts continued to create the better openings. Fox and Luongo were again involved, with the latter playing in his midfield partner, who shot straight at the keeper.
Moses Odubajo rattled the crossbar with a powerful effort from distance three minutes before half-time, but the Owls were quickly made to pay for their profligacy after the break.
Adam Reach gave the ball away and Bela's low cross from the right was turned in by Gimenez.
Harris wasted a glorious chance to equalise when he fired into the side-netting, but at the other end Jude Bellingham and Fran Villalba fired wide as the Blues continued to cause problems on the break.
Harris equalised nine minutes from time after Birmingham's defence stood off and he fired low into the corner after being allowed to run to the edge of the box unchallenged.
Tom Lees headed a Bannan free-kick straight at Trueman as the hosts pressed for a winner, and the Blues keeper had to pull off a fine save moments later to keep out Atdhe Nuhiu.
In a frenetic finish, Blues pair Lukas Jutkiewicz and Marc Roberts both cleared off their own line from corners but Wednesday could not find a winner.