Sheffield United 2, Birmingham City 1: Full time report
But it was Birmingham who looked the more likely to open the scoring, with Carlos Costly heading over the bar after 21 minutes.
And a minute later Scott Sinclair skipped past Morgan down the left and chipped over the advancing Kenny but his finish drifted away from goal.
United came close 12 minutes before the break when Henderson's header was cleared off the line by Carr and Webber headed the rebound straight at Maik Taylor.
But they were in front three minutes before half-time when Henderson headed the ball into the path of the unmarked Webber, who smashed the ball past Taylor.
Cameron Jerome replaced Honduras striker Costly at half-time and McLeish sent his players out early for the second half, but it was United who looked more sprightly in the opening exchanges of the second half.
Midfielder Stephen Quinn was as industrious as ever and Cotterill was proving to be a dangerous outlet.
Henderson had an opportunity to double United's lead after 56 minutes but was unable to get a good contact on Greg Halford's deep cross.
And two minutes later the former Watford striker was presented with another opportunity when Cotterill picked him out but his header looped wide of the target.
It was all one-way traffic and United came even closer to doubling their lead after 61 minutes when Matt Kilgallon's towering header was saved by Taylor and the ball fell into the path of skipper Morgan, who was denied by the Blues goalkeeper at point-blank range.
But the visitors were level with 17 minutes remaining with goal that came out of the blue.
Full-back David Murphy was allowed too much space on the left and United were made to pay as he whipped in an inviting cross that was turned into his own net by the unfortunate Morgan.
But the Blades restored their lead nine minutes from time when on-loan striker Beattie tumbled in the area following minimal contact from Carr and Jaidi.
And Cotterill held his nerve to send Taylor the wrong way from the spot.
