The loss will sting for the Storm, particularly after the gutsy effort after losing both prop Christian Welch and Brandon Smith through head injuries in the opening half.
The Panthers led 6-0 at the break, after a brilliant piece of vision from Nathan Cleary saw Stephen Crichton score in the corner and the half chipped the ball to the unmarked winger.
The Panthers' Brian To'o scored two minutes into the second half to make it 10-0 but it was far from over.
With 15 minutes to go, the Storm made it a four-point game with Ryan Papenhuyzen scoring next to the posts.
The Storm had been struggling to get any shot at the line and it took innocuous kick from Cameron Munster that beat Villiame Kikau for Papenhuyzen to close the scoreline to less than a converted try.
However, the Panthers held on, and moved on to the grand final.
Storm skipper Dale Finucane said he was disappointed by the result and said Melbourne "didn't give ourselves a genuine chance".
"We went into half time at 57 per cent completions," he said. "It was only 6-0 down, but we let ourselves down with completions tonight. I'm obviously not taking anything away from the Panthers, they were outstanding and have been all season. But it's a disappointing way to finish our season."
Speaking on ABC, Cameron Munster didn't hold back, saying: "It was one of the worst performances of the year, and unfortunately it was on the biggest stage."
Here's how the match unfolded: