That converted try gave Melbourne a 20-6 lead in the 64th minute which the visitors had no chance of pegging back.
But Slater wasn't finished, 10 minutes later putting a clever kick through for second rower Kevin Proctor to also score.
While the home side dominated the second stanza, the first half honours went to the Panthers, who ensured another slow start for Melbourne, after trailing last round 18-0 against the Eels.
The Storm didn't hit the front until the 46th minute through a penalty kick by their skipper Cameron Smith for an 8-6 lead.
The Panthers, who were desperate to break into the top eight with the finals beckoning, said they would treat this game like a grand final.
And they started with plenty of purpose.
Penrith's Adrian Purtell gave his side the lead in the sixth minute as the visitors sent the ball wide, with the centre scoring in the corner.
Seven minutes later, the home side crossed the tryline through Ryan Hinchcliffe after halfback Cooper Cronk drew the defence.
Penrith was unable to take advantage of four repeat sets to add to their tally and then rain started to fall late in the half, with errors creeping into both sides' games.
The Panthers couldn't maintain the rage in the second half as the Storm, thanks to Slater, woke from their slumber.
After Smith's penalty to break the deadlock, a bustling Sika Manu broke through the defence to crash over for a 14-6 lead which also seemed to break the Penrith spirit.
And it was all Storm from then.
MELBOURNE 26 (R Hinchcliffe S Manu K Proctor B Slater tries C Smith 5 goals) bt PENRITH 6 (A Purtell try L Walsh goal) at AAMI Park. Referee: Ben Cummins, Phil Haines. Crowd: 12,162.
- AAP