Former England captain, Charlotte Edward’s 78-run first-wicket stand with Suzie Bates saw the Vipers chase down 141.
Despite a middle-order wobble, seasoned internationals Sara McGlashan and Lydia Greenway powered the Vipers home with seven balls left at Chelmsford.
Current England skipper Heather Knight – who starred in the semi-final – could only score six as Storm posted 140-5.
Edwards played second fiddle to the attacking Bates and, having made a classy 24 off 18 balls, the ex-England international was bowled by Jodie Dibble.
Bates reached her half-century off 43 balls but Georgia Adams’ disastrous decision to call for a quick single saw the New Zealand captain run out.
However, McGlashan and Greenway remained calm as they took their side to victory in front of the 1,353 spectators in Essex.
With player of the tournament Taylor and Priest threatening to propel Storm is a huge first innings score, former England all-rounder Brindle induced a collapse as she had West Indies captain Taylor caught at mid-off.
Despite playing no professional cricket since 2014 prior to the Super League, Brindle continued her impressive form in the competition, having Knight caught at square leg.
The experience of the Vipers’ senior players told with Suzie Bates removing the dangerous Priest to stunt Storm’s progress as they lost 4-32.
Warwickshire all-rounder Georgia Hennessy blasted nine off three balls to give some late impetus to the innings but the total would prove to be little trouble for the impressive Vipers.