Isak's smart finish - his 50th goal for the club - put Eddie Howe's side ahead after 37 minutes at the Emirates Stadium, racking up his half century in just his 89th appearance in a black and white shirt.
It was his 14th goal in his last 15 outings for the Magpies, a remarkable run of form, and Gordon's tap-in after the break gave United a two-goal lead to carry back to St. James' Park for February's all-important second leg.
Newcastle were good value for their victory, too, bagging two opportunistic goals and protecting their lead thanks to an outstanding, committed defensive display which has left them just 90 minutes away from making sure of their return to Wembley for March's final.
Early brightness from the visitors led to an opening for Isak, who ran in behind and squared for Joelinton, who blazed over. At the other end, Gabriel Martinelli and then William Saliba both saw efforts blocked in quick succession, the latter by a sliding Dan Burn, in what was a high-tempo start.
Both sides continued to create chances. Jurrien Timber somehow headed a Declan Rice corner over from close range while Isak - who was causing the Gunners plenty of problems - centred for Lewis Hall whose shot was cleared, with Sandro Tonali then firing over from the edge of the box.
Just before the half hour mark, a golden chance to break the deadlock fell to the hosts. Leandro Trossard released Martinelli with a neat first-time through ball and the Brazilian winger accelerated past Sven Botman, but his strike thumped the post and bounced away to safety.
After another opportunity for Mikel Arteta's men - a scramble in the box that culminated in a superb block from Botman to deny Kai Havertz - the Magpies went up the other end at seized the advantage. It came from a long free kick from goalkeeper Martin Dúbravka, which was flicked on by Botman and nudged into Isak's path by Jacob Murphy. The Swedish forward was well onside and his finish was unerring, arrowed over David Raya and in off the crossbar.
Dúbravka produced a fine stop in the half's closing stages, smothering centre back Gabriel's goalbound shot from close range, but five minutes after the restart, the Magpies moved further in front. Isak had a hand in the build up, playing the ball out wide to Murphy before receiving it again in the box. His shot was tipped away by Raya but only as far as Gordon, who arrived at just the right time to apply the finishing touch in front of 6,000 travelling fans.
Before the hour, Havertz squandered a clear-cut chance to pull one back, turning the ball wide with his shoulder after Trossard's cross had deflected off Hall and into his path right in front of goal. Rice then had a go, arriving late in the box, but the Gunners still couldn't profit from it. Saliba climbed highest to meet a corner once more, but again, he headed over with the goal gaping.
Substitute Jorginho was denied by a timely Joelinton block and Martinelli set himself up before volleying over as Arsenal applied pressure, but it was to no avail as the Magpies stood firm to record a vital clean sheet ahead.
All eyes will be on the second leg now on Wednesday, 5th February, where Howe's men will look to book a Wembley return in front of a raucous home crowd at St. James' Park.
