Newcastle had not won away to Arsenal since November 2010 and were without key duo Bruno Guimaraes and Fabian Schar through suspension, but they defended resolutely to hold on to a two-goal lead as the hosts continued to struggle in front of goal.
This result gives Newcastle a great chance to qualify for the final. The second leg of the semi-final will take place on February 5, where Newcastle will have the advantage of playing at home.
Kai Havertz, picked to start in place of the in-form Gabriel Jesus, missed their best chance when he headed wide from close range.
Arsenal head coach Mikel Arteta told Sky Sports: "The biggest difference was the intensity of the game. In every other aspect, we were the better team. They scored two goals, they deserve credit for winning the game in that way. We created a lot of chances, but the truth is they defended very well in the box.
We can do better with our decisions. We had one-on-one chances with the goalkeeper; in the semi-final you have to be decisive in your decisions.”
The Spanish strategist was not surprised when Isak scored. The Swedish striker has been in great form recently. He took advantage of a chaotic moment in Arsenal's defense to punish the home team.
On the return leg, Arteta said: “We have to be disappointed with the match because it was a result we didn’t want, but that’s the reality. I have full faith in Arsenal. I saw the way the players played against them, I believe we can turn the game around in the second leg.”
Meanwhile, Newcastle manager Eddie Howe said: “It was a tough game for us and today’s win shows a big step forward for Newcastle, especially when you look at our recent away form.
We are playing with confidence, which helps when the team defends in decisive moments. The game is still very attractive, it is still very balanced. We have a difficult home game coming up. We will have the support of the fans and need to do everything right to win in the end."
