Delhi captain Meg Lanning elected to bat after winning the toss and the Australia skipper top-scored for her side with 35 as the Capitals managed a modest 131-9.
Even that score had looked improbable after they slumped to 79-9 but Shikha Pandey and Radha Yadav smashed unbeaten breezy 27s to give Delhi bowlers something to defend.
Mumbai lost both the openers early but skipper Harmanpreet Kaur (37) and England all-rounder Sciver-Brunt combined in a 72-run stand to put their team on course for victory.
Sciver-Brunt, the league's most expensive foreign recruit along with Australia's Ashleigh Gardner, sealed victory in the final over with a paddle shot that raced to the boundary.
"Over the moon," Mumbai coach and former England captain Charlotte Edwards said when asked for her reaction.
"To win this is one of my greatest achievements in my career.
"They (players) played for one another, it has been a wonderful experience."
The five-team tournament has been hailed as a 'game-changer' in women's cricket, offering lucrative deals to attract the leading names.
The sale of WPL's franchises and media rights alone fetched $690million and the organising Indian cricket board lined up an impressive array of sponsors for the 22-match tournament.
