The Storm fired a last shot when Will Chambers crashed over but it was all too late - the South Sydney defence which had held for much of the game rewarded with a deserved victory, their first over the Storm in Sydney since 2004 and just their fourth finals win since 1971.
It leaves Melbourne to face the winner of Sunday's Canterbury-Newcastle elimination final in a sudden-death semi-final next weekend.
The Rabbitohs can put up their heels, having taken advantage of their chances in the opening period before leaning on a defence which had been carved up last week by the Sydney Roosters to take a 14-0 halftime lead.
It was a nervous Bunnies side early with a penalty and early Sam Burgess knock-on, but Burgess repaid his team when he came up with the hit which forced Justin O'Neill to spill the ball - Adam Reynolds spreading it to an unmarked Farrell to cross out wide.
Lima got over the line through sheer will power as the Storm's discipline went out the window via five straight penalties, Sisa Waqa denied a reply when Farrell held him up in the in-goal just before the break.
It was a different Storm after the break with Slater scoring off the back of a scrum win, but when he was denied a second, it was all over for the visitors.
The Storm will be hoping for some good news on Waqa after he fell heavily on his head late in the contest in an incident which saw Farrell placed on report.
Earlier, Souths prop Roy Asotasi was placed on report for a questionable crusher tackle on Jason Ryles.
Rabbitohs coach Michael Maguire pointed to his side's defence as the key, and was adamant they are ready to improve on last year's preliminary final loss.
"As a squad we're 12 months down the track from where we were," Maguire said.
"I think we're a much improved team from this time last year, that's for sure."
Storm mentor Craig Bellamy was left lamenting the Slater no-try call that went against his side.
"He said (the referee) Will took Merritt out - at the same time I think Goodwin was escorting Will and knocked him off balance so Will couldn't have a proper shot at the ball," Bellamy said.
"I don't think Will intentionally went in there to take him out.
"I think that was a real tough call actually."
Storm skipper Cameron Smith admitted the time had come for his side to make a stand.
"We need to make a decision as a team where we want to go now for the rest of the season," Smith said.
"We've got three possible games, we've got to turn it around real quick from that performance tonight."
- AAP