The hosts held the advantage at the break thanks to a Declan Rice goal after 34 minutes, but the Cherries turned the game around in the second half.
Dean Huijsen equalised with a fantastic header from an Antoine Semenyo long throw, before Evanilson netted his 12th goal of the season, bundling home from a corner with 15 minutes to play.
And the Cherries saw out the remainder of the fixture to make history in north London.
Andoni Iraola surprised a few with his team selection, opting to give Antoine Semenyo a well-deserved rest in one of three changes.
Marcus Tavernier came in for the Ghanaian, while Julian Araujo and Lewis Cook also started, in place of Adam Smith and Alex Scott.
_(Image: John Walton/PA Wire)_ Mikel Arteta, meanwhile, named a strong Arsenal side in between their two Champions League semifinal legs, with just two changes from the side that were beaten 1-0 by PSG in the first leg.
The two sides sought some early control as attacks were few and far between in the opening 15 minutes.
The first effort on goal came just before the 15-minute mark and it fell the way of the hosts, Rice slipped in behind by Gabriel Martinelli, but the Englishman dragged his shot wide of the far corner.
Rice had another opportunity two minutes later but miscued his shot wide again, before Bukayo Saka threaded a pass through for Ben White in behind, his clipped cross headed behind by Illia Zabarnyi with Rice threatening.
_(Image: John Walton/PA Wire)_ The Cherries first chance of the game fell to striker Evanilson in the 26th minute, but he wasn’t able to get enough height on his jump to keep his header down.
Martinelli dragged a shot wide after he was teed up on the edge of the box by Saka, before Kepa made a good save from a Leandro Trossard header.
Arsenal took the lead after 34 minutes, Rice slid in behind by Martin Odegaard and rounding Kepa before finishing from the angle despite the best efforts of Zabarnyi.
Justin Kluivert went close after he drove at the defence and shot from just outside the box, his deflected effort not far from the top corner.
_(Image: John Walton/PA Wire)_ Evanilson attempted to chip David Raya after the keeper gave the ball away but his effort was just too high as the hosts led at the break.
As in the first half, there were few chances in the opening exchanges of the second period, the hosts squandering a five-on-five on the break early on.
A Milos Kerkez cross was not far away from Tavernier arriving at the far post before the left back blocked an effort from Saka at the other end.
Kepa caught comfortably from a Saka header, before the Englishman curled an effort past the Spaniard’s far post.
Dango Ouattara did brilliantly to beat his man on the left but his cross was too close to Raya, with Iraola going to his bench shortly after the hour mark.
Semenyo and Scott replaced Kluivert and Araujo, and the Ghanaian’s first action was to be slipped in behind, winning a throw in after a heavy touch.
_(Image: John Walton/PA Wire)_ But Semenyo launched the throw into the Arsenal box where Huijsen rose to flick his header into the far corner and draw the Cherries level brilliantly after 67 minutes.
David Brooks replaced Ouattara before the Cherries took the lead with 15 minutes to play.
Scott swung in a corner which was met by Tavernier with a free header, who flicked it on for Evanilson to bundle home at the far post, the goal given after a check for handball by VAR.
Daniel Jebbison replaced the Brazilian with three minutes left of the 90, and the Cherries saw out six added minutes to complete their first ever league double over Arsenal.
**Arsenal:** 22, David Raya; 49, M. Lewis-Skelly; 15, J. Kiwior; 2, W. Saliba; 4, B. White (O. Zinchenko 86’); 41, D. Rice (M. Merino 74’); 5, T. Partey; 8, M. Ødegaard (c); 11, G. Martinelli (R. Sterling 86’); 19, L. Trossard; 7, B. Saka (E. Nwaneri 86’).
**AFC Bournemouth:** 13, Kepa; 3, M. Kerkez; 2, Dean Huijsen; 27, I. Zabarnyi; 22, J. Araujo (A. Scott 65’); 12, T. Adams; 4, L. Cook (c); 11, D. Ouattara (booked, 64’)(D. Brooks 74’); 19, J. Kluivert (A. Semenyo 65’); 16, M. Tavernier; 9, Evanilson (booked, 58’)(D. Jebbison 87’).