Isak struck shortly before halftime in the first leg of the semifinal at a chilly Emirates Stadium and then had a big role in Newcastle’s second, scored by Anthony Gordon after the break.
Arsenal were left to rue their failure to convert several good chances with Gabriel Martinelli denied by the woodwork in the first half and Kai Havertz missing a golden opportunity.
In-form Newcastle, who have not won a major trophy since 1955, will now be clear favourites to complete the job in the second leg on Tyneside next month.
Tottenham Hotspur host holders Liverpool in the first leg of the other semifinal tomorrow.
Arsenal had been unbeaten in their previous 13 games in all competitions, but were not at their best against a clinical Newcastle side who have taken a liking to north London.
Three days ago they won 2-1 at Tottenham to move closer to the Premier League’s top four and they returned to send the travelling Toon Army back up north in high spirits.
Isak has been virtually unstoppable of late and he has now scored 10 goals in his last nine appearances for the club.
The Swede lofted one early half-chance over the crossbar but showed how lethal he is after 37 minutes when a long ball into the area fell into his path and he fired the ball high past David Raya into the roof of the net.
It brought up the 25-year-old’s half century in just 89 matches for the club, five games fewer than it took Newcastle great Alan Shearer.
“First half he was electric, I thought he played really well. He scored but I just thought his general game was in a really good place,” Newcastle manager Eddie Howe said.
Arsenal had threatened with Martinelli curling a shot against the post from the edge of the area and Newcastle were forced into some desperate defending in one goalmouth scramble.
Jurrien Timber also headed over the crossbar from close range for the hosts and Havertz was even more culpable after the break when he somehow failed to connect with a header with the goal gaping, the ball bouncing off his shoulder.
By that time, Newcastle were 2-0 ahead thanks to a tap-in by Gordon in the 50th minute. Jacob Murphy threaded a great pass to Isak in the penalty area and his first-time shot was only parried by Raya for Gordon to sweep in the rebound.
Arsenal, who had 23 shots to Newcastle’s seven, piled on the pressure late on to try to reduce the deficit but Newcastle manned the barricades to take a healthy lead to St James’ Park.
“In every other aspect we were the better team but it’s about scoring goals,” Arsenal manager Mikel Arteta said.
“Credit to them, they defended their box very well. We had the chances but at this stage, a semifinal, you have to be clinical.”