An own goal from Ben White and then a late strike from January signing Bruno Guimarães sealed the win for Newcastle and left Arsenal two points off Tottenham Hotspur in fourth in the standings with one game of the season remaining.
Thanks to their superior goal difference, Spurs will only need a point at already-relegated bottom side Norwich City on Sunday to qualify for Europe's elite competition. Mikel Arteta's side face his former team Everton at home at the same time.
Newcastle started brightly, roared on by their fans in their last home game of the season. Eddie Howe's side were in the bottom three at Christmas but thanks to their new owners' spending in the January transfer window, have climbed up the table and only lost once at home in the league in 2022.
They dominated the match and came close to opening the scoring in the 37th minute through Allan Saint-Maximin, who cut in from the wing and jinked his way to the edge of area, but saw his low shot palmed away by goalkeeper Aaron Ramsdale.
The breakthrough came shortly after halftime, however, when Joelinton powered down the left wing and sent in a low cross for striker Callum Wilson but it came off Arsenal defender White and into his own net.
The hosts had plenty of chances to double their lead and finally did in the 85th minute when Wilson ran through on goal but the ball ricocheted off Ramsdale into the path of Guimareas who side-footed it in.
The win, Newcastle's first in the league over Arsenal since April 2018, means Howe's side move up to 12th in the standings.
Arsenal manager Arteta conceded his side were deservedly beaten.
"Newcastle deserved to win the match and were much better than us. We had nothing in the game. They were much better in every department and we were poor with the ball," he told Sky Sports.
"A lot of things happened during the game, like substitutions for injuries, but it's not an excuse because they were much better than us.
"It's true that we could not cope with the game that we had to play here. We tried to change some things but it didn't make it better. We had moments where we looked better but then the execution was so poor and the goals we gave away were extremely poor."