The Gunners fell behind within a couple of minutes to Samantha Kerr but responded through Stina Blackstenius, Kim Little and a Niamh Charles own goal in a sterling tactical display.
Emma Hayes's side could hardly have got off to a brighter start at Selhurst Park, as Kerr headed the reigning Women's Super League champions in front from Guro Reiten's delivery with just two minutes on the clock.
However, Arsenal responded brilliantly to that early setback and were deservedly level with 14 minutes on the clock, as Blackstenius was in the right place at the right time to latch onto Magdalena Eriksson's unfortunate deflection and sweep home from close range.
With co-owner Todd Boehly in attendance, things went from bad to worse for Chelsea in the 24th minute, as Katie McCabe was felled by Sophie Ingle inside the box, and Little stepped up to convert from 12 yards.
Jonas Eidevall's side were in a ruthless mood at Selhurst Park and had the ball in the back of the net for the third time in the 35th minute, but Blackstenius had strayed just offside when she latched onto Steph Catley's through ball.
The ever-dangerous Reiten to Kerr combination led to the latter heading wide in the 41st minute as Chelsea tried to turn the tide, but that missed chance would haunt her, as a stoppage-time free kick from Catley was turned into her own net by Charles to give Arsenal a two-goal cushion at the break.
Hayes's half-time team talk did little to galvanise Chelsea, who somehow avoided giving away another penalty when Kadeisha Buchanan tripped Catley inside the area on the hour mark, but referee Kirsty Dowle pointed for a corner instead.
Chelsea could not capitalise on that inexplicable reprieve, but substitute Melanie Leupolz saw a cross-cum-shot deflected onto the bar by Manuela Zinsberger in the 86th minute.
Nevertheless, Arsenal never looked like ceding their two-goal advantage and saw out a well-deserved two-goal win to add to their League Cup triumphs from 2011, 2012, 2013, 2015 and 2018.
Meanwhile, Chelsea - champions in 2019 and 2020 - have now lost back-to-back finals after going down to Manchester City in the showpiece match last season.