Olivier Giroud bagged a first-half brace as the Gunners looked in cruise control going into the half-time break.
Urged on by their fans, the Magpies responded and reduced the arrears through Moussa Sissoko early in the second half, but they fell short in their comeback bid.
Below, Sports Mole analyses how the North Londoners survived a second-half onslaught to maintain their momentum in the race for Champions League qualification.
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On target: 4
On target: 3
Was the result fair?
While Newcastle deserve plenty of credit for the heart shown in their second-half onslaught, they did not do enough in the final third to merit a point, having forced goalkeeper David Ospina into just one notable save throughout their dominant 45-minute spell. The visitors' defence was superb at the end of what has been a disappointing week and it would have been harsh on them had they not held on for the victory.
You need only have heard the boos that echoed around St James' Park at half time to realise that Newcastle fans were furious with their side's first-half performance - and rightly so. John Carver's side were outplayed for much of it and could have easily gone into the break with more than a two-goal deficit.
With right-back Ryan Taylor recently returning from long-term injury, and Jack Colback operating in an unfamiliar left-back role by virtue of Newcastle's depleted squad, the duo struggled to contain the likes of wingers Danny Welbeck and Alexis Sanchez regularly, while Ayoze Perez offered very little up the other end of the field.
Did they improve after the break? Immeasurably. Newcastle emerged brilliantly from the interval and reminded us how true the adage 'a game of two halves' can be. The home supporters acted as a 12th man for their team on the comeback trail as they cranked up the volume and urged Newcastle on at every given moment, with Sissoko's 49th-minute strike offering them real hope.
While their momentum seldom waned, they struggled in the final third against a resolute Arsenal defence that refused to give Carver's side an inch after Sissoko's effort and, in the end, they fell short.
After bowing out of the Champions League on away goals to Monaco in midweek, manager Arsene Wenger will have demanded that his troops refuse to allow their European disappointment to hinder them in the quest for another top-four finish.
Wenger will have got his wish after watching his side produce a first-half display with plenty of brio to quell fears of a hangover, as Giroud struck twice to give his side a deserved 2-0 lead at the break.
Consequently, one or two of the Arsenal players could have been forgiven for thinking that the second half represented a chance to boost their goal difference, but things did not quite pan out that way as the visitors' defence found themselves under intense pressure from the 49th minute onwards.
It acted as the perfect wake-up call, though, as Arsenal's back four stood up well to the task of preserving their lead by repelling attack after attack, with Ospina only having to make one notable save throughout the half.
It was not vintage Arsenal, but the resilient manner of the win will have softened the blow of their Champions League exit, and they remain on course to do it all again next season.
Sports Mole's man of the match
Olivier Giroud: It probably has to be the towering Frenchman, whose first-half brace proved the difference. He was not always involved, and looked particularly quiet in the second half, but decisiveness has been a regular theme of his performances this season and he came up with the goods here again.
Charged with the task of man-marking Giroud, Mike Williamson's defending was questionable for both of Arsenal's first-half goals, but the second looked particularly incompetent as the Gunners striker easily held off his half-hearted challenge to head the visitors into a 2-0 lead without even jumping.
Perhaps Williamson is the reason why Giroud - who has eight goals in six games against United - likes playing Newcastle so much.
Mike Jones had a quiet game. There were one or two penalty appeals by Newcastle players that he had to contend with, but replays showed that he made the right decision on each occasion. Good performance overall.
Newcastle: United will enjoy a 15-day recovery period due to the international break as they look forward to a local derby with bitter North-East rivals Sunderland on April 5.
Arsenal: Wenger and company face top-four rivals Liverpool at the Emirates on April 4.