The Gunners led from the outset after skipper Steph Hughton broke the deadlock inside two minutes, heading home a neat cross from Rachel Yankey.
The Super League champions failed to add to their lead in the first half despite dominating play and seeing Jordan Nobbs hit the woodwork.
But Nobbs would get on the scoresheet with a header of her own late in the second 45 before Ellen White made absolutely certain shortly afterward.
The cup win is Shelley Kerr’s first trophy as coach, having taken charge at Arsenal Ladies just four months prior.
She said after the result: We have been so successful in the past and the expectations have been so high.
"For me it's all about the players - they have been exceptional today. Before the game, I just said to them 'relax'.
“We have been playing good football and sometimes you just have to be patient to get results. I thought we won comfortably in the end."
Making matters worse for Bristol, who also lost to Arsenal in the 2011 final, midfielder Lucy Staniforth was stretchered off in the second half with what appeared to be a very bad knee injury.
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