Swiss international Ramona Bachmann scored their first two goals in the 48th and 60th minutes before Vivianne Miedema from the Netherlands pulled one back.
Fran Kirby, the Women's Footballer of the Year, restored the two-goal lead within three minutes.
Arsenal had previously won the trophy 14 times, including beating their London rivals in the 2016 final.
Chelsea captain Katie Chapman earned her 10th winners' medal.
Their manager Emma Hayes, eight months pregnant with twins, took her place on the touchline but had decided not to lead the team out in the hot weather.
(Reporting by Steve Tongue, editing by Pritha Sarkar)
