Ahead of a proposed move to India, Cummings became just the second man to score a treble in an A-League Grand Final, while efforts from Moresche, Beni Nkololo and Samuel Silvera also flew past Tom Glover in the City goal during an extraordinary demolition job.
Rado Vidosic's side briefly gave themselves hope through Richard van der Venne's volley, but the premiers suffered a catastrophic collapse after the break as they suffered a third Grand Final loss in four years.
While Melbourne City saw more of the ball early doors, the reigning premiers showed a propensity for mistakes, and one such error from Valon Berisha nearly proved costly with just nine minutes gone.
After the Reims loanee lost the ball in a dangerous area in the ninth minute, Marco Tulio slipped through Cummings, but Glover's outstretched hand took the pace off his effort before Curtis Good hacked the ball away as it was trickling in.
The Mariners kept asking questions of the City backline, though, and Cummings had a second bite at the cherry in the 20th minute - one which the 28-year-old did not pass up.
Latching onto a cross from Nkololo, Cummings's first attempt on the volley was blocked by Good, but the Mariners striker bulldozed his way past the 30-year-old to poke home the rebound.
Injury was soon added to insult for Melbourne City as Berisha's race was run in the 22nd minute - the Kosovan had been clattered into by Mariners goalkeeper Danny Vukovic a few moments before Cummings's opener and could not shake off the effects of that exchange.
Things would go from bad to worse for Vidosic's charges with 34 minutes gone, as Cummings went from goalscorer to provider - holding up the ball in the middle of the pitch and releasing Silvera, who left Nuno Reis in his wake on the left flank before advancing into the box and picking out the bottom corner with panache.
The Mariners' two-goal lead may have seemed too good to be true for some of the Coasties faithful, and it briefly proved to be the case, as Melbourne City cut the deficit in half five minutes before the break.
Despite being surrounded by a sea of yellow and blue shirts, Good fed Jamie MacLaren in the left-hand side of the box, and the 29-year-old cut back for the arriving Van der Venne to direct a sublime side-footed volley into the roof of the net.
City's defensive deficiencies very nearly came back to haunt them in added time, though, as Nkololo ghosted into the box to latch onto Tulio's delicate pass, but in trying to find the bottom corner, he was denied by the outstretched boot of Glover, who proceeded to give his backline quite the earful.
Melbourne City were indebted to Glover for keeping the scoreline respectable at half time, but the premiers' number one had little to do in the first 15 minutes of the second half, as the Mariners absorbed constant pressure from Vidosic's side.
City struggled to create anything meaningful, though, and an inspired substitution from Montgomery worked wonders not long after, as the Mariners were awarded a penalty for Andrew Nabbout's inexcusable kick on the recently-introduced Jacob Farrell.
Cummings stepped up and coolly doubled his tally for the day in the 65th minute - sending Glover the wrong way with a calm finish into the bottom corner - and just seven minutes after their first spot kick, Farrell engineered another penalty for the marvellous Mariners.
The 20-year-old got to the byline inside the box and attempted to cut back for a teammate, but his cross struck the hand of a sliding Callum Talbot, who had barely been on the pitch for a couple of minutes before giving away the game's second spot kick.
Having opted for placement on his first penalty, Cummings went for the top-right corner this time around, and the striker converted with aplomb to complete a terrific treble.
Melbourne City were already resigned to defeat, but the premiers' evening became even more humiliating in the 84th minute, as Silvera's sumptuous outside-of-the-foot cross was on the money for Nkololo to head home the Mariners' fifth.
The embarrassment would not end there for Melbourne City, as in the first minute of added time, substitute Moresche cut onto his right foot inside the box and bent a delightful strike into the bottom corner before the Coasties revelled in an exceptional Grand Final triumph at full time.
The Mariners have now ended a 10-year drought without an A-League crown after their maiden success in 2013, while Melbourne City now have Grand Final defeats to their name from the 2020, 2022 and 2023 showpiece events.