Switzerland international Bachmann broke the deadlock three minutes into the second half with a neat finish after being set up by Kirby.
Bachmann soon curled home a second, via a slight deflection, before Arsenal pulled a goal back through Vivianne Miedema in the 74th minute.
England forward Kirby, though, ended any hopes of a recovery when she swiftly netted a third Chelsea goal as the Blues gained revenge for their 2016 final defeat in front of a record crowd of 45,423.
Cuthbert was a second-half substitute for Chelsea, while her Scotland international team-mates Kim Little, Lisa Evans and Emma Mitchell were in the Arsenal starting line-up.
Chelsea Ladies could yet go on to claim the Double as they look to edge ahead of rivals Manchester City, whom they beat in the FA Cup semi-final, over the closing weeks of the Women’s Super League.
Arsenal have won the FA Cup a record 14 times but were second best yesterday.