Wing Suliasi Vunivalu also continued his love affair at Brookvale.
Returning to the same ground where he scored four tries last year, he bagged two of the first half's nine four-pointers, and set up another.
After running on to a Slater ball to open the scoring, he crossed for another from a Cooper Cronk cross-field kick, then put fellow winger Josh Addo-Carr in after skirting down the touchline.
Melbourne should have been in control of the match after scoring four tries in the opening 18 minutes, but Cameron Smith landed only one conversion. It allowed Manly back into the match when Frank Winterstein and Jorge Taufua scored, while centre Kelly crossed after the halftime siren to shift the momentum.
Jake Trbojevic continued the comeback in the second half when he bolted on to a spiralling ball from brother Tom, and a grandstand finish was on when Akuila Uate leapt on to a Daly Cherry-Evans bomb to put Lawrence over in the 66th minute.
But Melbourne's experience and class stood up, forcing two line dropouts in the final five minutes to claim their sixth win of the season.
St George Illawarra staved off a furious second-half comeback from North Queensland to hold on for a 28-22 victory and cement their spot at the top of the NRL table. The Dragons surged to a commanding 28-4 halftime lead before the Cowboys scored three straight tries to get within six points with 16 minutes remaining.
The home side held on to secure their fifth victory on the trot and hold pole position for the first time in three years. Centre Tim Lafai bagged a double, while Gareth Widdop continued his stellar start to the season.