The premiers haven't always been pretty on a winning run that stretches seven matches but they did enough again at Mt Smart Stadium on Sunday.
In a far cry from their 50-10 win over the Warriors on Anzac Day, Melbourne relied on defensive scrambling, slightly better control and some fortunate referee calls to join South Sydney and St George Illawarra on 13 wins.
A superior points differential puts them on top and on target to repeat their minor premiership win in 2017.
The Storm welcomed back a swag of Origin players but struggled to bust open a Warriors side who have lost four successive matches at their home ground.
First-half tries down the right edge to Will Chambers and Suliasi Vunivalu put them 8-6 up at the break.
They set up another narrow triumph, having won three of their previous six games by one point.
The Warriors missed the control of injured five-eighth Blake Green while they also lacked direction for much of the second half without hooker Issac Luke, who exited with an injury.
Gerard Beale scored the only Warriors try, when winger David Fusitu'a also soared to claim a cross-kick.
The hosts went close soon after the break through Kata, who was penalised for a double movement.
The Storm closed ranks and pulled clear through penalties to Cameron Smith in the 56th and 78th minutes before repelling a late Warriors attack.
It was the Warriors' sixth-straight loss to the Storm, leaving the Kiwi outfit eighth and under pressure from the in-form Wests Tigers in ninth, four points back.