Tony Mowbray's team won at St Andrew's while the other team lost.
The Wearsiders' first goal was set up by Amad Diallo.
Blues' first home defeat since August seemed to be sealed four minutes into the second half when Diallo scored.
Substitute Lukas Jutkiewicz gave the Blues hope on 78 minutes with his first goal in almost a year, but it wasn't enough.
It was enough for the Wearsiders to leapfrog the Blues into the top half of the table thanks to a second straight away win.
If Blues had won, they would have climbed into the top six of the Championship.
When Troy Deeney's head bounced back off the left upright and bar, they missed a great chance.
Diallo looked like he had been stopped on the edge of the penalty area, but he powered himself back off one knee to twist himself out of the tackle, and the distracted Blues defence were caught flatfooted.
Scott Hogan, the top scorer for Blues, had a great chance to score at the end of the first half.
The visitors' lead was doubled when Diallo stole into the right side of the Blues box and, just when he seemed to be closed down, he unleashed a superb left-foot curler which dipped just inside John Ruddy's right post.
Jutkiewicz's introduction on 59 minutes in a triple substitution that also brought on George Hall and also ended Jobe Bellingham's evening on his first start, was always going to have an effect.
It brought only one goal as Jutkiewicz steered into the far corner after Bailey Wright missed his kick and the visitors hung on.
The World Cup break will give the Championship teams the shortest wait for their next games.
The game against Millwall is only 22 days away.
On Saturday, 10 December, the Blues will be on the road for an away game.
John Eustace spoke to the radio station.
We didn't lose enough duels. The subs made a difference when they came on, even though we weren't as sharp as we have been.
The last run of games has taken a lot out of us, but I still don't think we deserved to lose.
Lukas has had to be patient, but I'm happy he got his first goal of the season.
We wanted to see what Jobe could do from the beginning and he did well.
Tony said on the radio that he was from Durham.
The players and fans came away with the three points, so I'm happy for them.
It was more of a case of digging in. I've known him since I signed him for Middlesbrough.
"I knew he'd cause us some problems, and in the end we were hanging on a bit, and Patterson made a great save," he said.
It has been great to see Diallo here. He has real talent. He only left when he got caught in the eye and couldn't see anything.
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