One year on from last year's grand-final defeat to Penrith, the Storm were electric in attack on Friday night against a resilient Sharks side who hung on until late.
Melbourne will now face the winner of four-time defending premiers Penrith and Brisbane in Sunday's other preliminary final at Suncorp Stadium.
The Storm have not won a premiership since Cameron Smith's retirement after the 2020 grand final, with the new era desperate to claim a title of their own.
And on Friday night, they led the way.
Cameron Munster and Ryan Papenhuyzen were dangerous with every touch, while Jahrome Hughes scored a try just 22 days after fracturing his forearm.
And with Cronulla doing their best to hang in there at 18-10 with five minutes to go, it was Grant who provided the knockout blow for the hosts.
Running it on the last, the Melbourne hooker got into free space and spread the ball to the left before Xavier Coates crossed and broke Sharks hearts.
Cronulla have defied their critics all season, and spent large parts of the match doing their best to repel a Storm side who always looked the better team.
Playing with a heavily protected left arm and defending on the wing at different stages, Hughes had his fingerprints all over Melbourne's win.
He copped a hit from Teig Wilton in the lead up to Melbourne's first try, and was on the receiving end of a high shot from Braydon Trindall in the second half.
But he still had his way, getting the ball out wide after the Wilton hit and allowing Nick Meaney to send Will Warbrick over for the Storm's first.
The halfback then scored Melbourne's next, when Stefano Utoikamanu continued his powerful end to the season by bumping off a defender and offloading to his halfback.
Hughes was able to fend of Jesse Colquhoun with his left arm, before breaking into space and going 30 metres to score.
And while Cronulla got back to 10-8, it was Munster and Papenhuyzen who landed the decisive blow before halftime when they caught Sharks fullback Will Kennedy up in the line.
Munster kicked early, before a chasing Papenhuyzen got to the ball first, toed ahead and then beat Kennedy to the line to dive onto it and make it 16-8.
Papenhuyzen also produced a vital try-saver on Briton Nikora midway through the second half, albeit while conceding a high-tackle penalty in the process.
That got Cronulla back in the game at 16-10, but another penalty allowed Melbourne to go out to an eight-point lead before Coates' match-sealing try.
Cronulla also had their moments, with Sione Katoa scoring a first-half double and Blayke Brailey again effective out of dummy-half.
And while KL Iro got a last-minute consolation try, the Sharks were ultimately outgunned by a Storm side who look like they can threaten whoever they meet next Sunday.
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