The 20-year-old proved the difference for the holders and grabbed the opener in the 109th minute after the tie had gone to extra time.
It could have been a different ending for academy gradate Smith Rowe had the video assistant referee not told referee Chris Kavanagh to review a decision deep into stoppage time.
The Geordie scored his first goal for the club in 10 years during last weekend’s home defeat to Leicester and could have added to his tally first in the 56th minute, when he side-footed a Jeff Hendrick cross wide, and let an even better chance slip in stoppage time when he failed to beat Bernd Leno from close range.
Bruce said: “When you come here, especially for a cup tie, and when you are presented with the opportunities we had, you hope you can take them.
“I couldn’t be more pleased with how they went about their work but we just needed to take the big opportunity when it came along.
“Nobody is more disappointed than Andy that he didn’t take one, but his overall play and the way he led the line was terrific. It would have capped a great week for him.”