Gloucestershire won the toss and elected to field, making a superb start when captain Lauren Parfitt was dismissed for just eight after being caught by Amelie Munday off Charlie Phillips.
A comical run out soon followed as Daisy Jeanes was dismissed but some impressive batting by Sturge and Gammon put Glamorgan in control.
They added 79 runs until Phillips finally made the breakthrough that Gloucestershire desperately needed, Sturge caught at deep point to leave the hosts 105-3.
The wickets then began to tumble with captain Liv Daniels claiming the pick of the bunch when catching Scottish international Megan McColl off her own bowling.
Daisy Mullan was next to fall as Phillips claimed her sixth wicket of the day and the hard-hitting Gammon fell for 69 in the final over as Glamorgan finished with 154-6.
Chasing a target of 155, Gloucestershire got off to the worst possible start.
Munday, who was the hero of the semi-final with 71, was bowled for a first-ball duck by Gemma Porter.
Porter soon got her second victim when Reddy hit one high to mid-wicket as Gloucestershire managed just 29 in the powerplay.
Glamorgan’s bowlers kept applying pressure until Patel produced an astonishing display to swing momentum in the favour of the visitors.
A disastrous over increased the tension when Sara Phillips was taken off after bowling a second high no-ball. Her replacement Megan McColl made the same mistake, with 19 runs coming off the over to increase the pressure on Glamorgan.
Eight boundaries and dropped catches from the home fielders ensured a dramatic finish at Sophia Gardens, before three quick wickets put Glamorgan on the brink.
Gloucestershire were bowled out for 122 when Patel skied a shot that was caught by Phillips, as Glamorgan won their first piece of silverware before becoming a professional outfit next season.