Jo Love gave Celtic the lead on 22 minutes, in front of a crowd of over 500 at Ainslie Park, Edinburgh. Controlling Rebecca Bisland's cross, she volleyed home the first of her brace.
It was 2-0 by the break, after Christie Murray doubled the Hoops' advantage with a 20-yard strike on 39 minutes.
Murray added another timely goal, 6 minutes after the restart, chipping keeper Jo Hutchison from the edge of the box.
Love made it 4-0 on 58 minutes, Suzanne Grant picking her out with a pass, which she lifted over the out-rushing keeper and turned in after a rebound off the bar.
Claire Crosbie netted a consolation goal for Spartans on 85 minutes but Celtic were able to celebrate a first cup in only their fourth year.
Pictured: Celtic celebrate second goal (above), Jo Love is denied by Jo Hutchison (right). (Lorraine Hill)