Black Cats star Sebastian Larsson cancelled out an early opener from Luis Suarez.
Bruce said: “We got away with it a little bit in the first 20 minutes, we gave the ball away badly. But we got over that period and the longer the game went on the more belief we had.
“We posed a bit of a threat and kept the ball better second half. I think that was key, we had to keep the ball better. All in all, it was a really good performance and I’m very pleased.”
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.