The Storm faltered during the first half and the score was tied 10-10 at halftime before 14 unanswered points sealed the result.
As in their heart-breaking first-round loss to the Roosters, the Rabbitohs toiled hard but again finished empty-handed.
An error by Slater led to one of South's tries but he more than compensated for that by setting up two Storm four-pointers as well as the two of his own.
In yesterday's earlier round two matches, coaches Wayne Bennett and Ivan Cleary bagged their first wins with their new clubs.
Newcastle gave Bennett his first win as Knights boss but it may have come at a heavy price as skipper Kurt Gidley has a possibly serious shoulder injury after yesterday's 18-6 win over a wasteful Cronulla.
Gidley departed in the sixth minute after dislocating his shoulder in an attempted tackle on Todd Carney.
The blow will be a concern for Bennett as the Knights continue to adjust to his reign, but the veteran mentor would have been happy with the resolve of his men who won handsomely without their leader and with only two fit players on the bench for the majority of time.
The injury-ravaged Panthers boosted coach Cleary - who finished with the Warriors last season - with a solid 18-0 victory over the Roosters.
Penrith showed few weaknesses, halfback Luke Walsh guiding his team smartly and centre Michael Jennings scoring twice.
But Roosters coach Brian Smith was aggrieved at what he claimed was the over-use of wrestling by Penrith's players in an attempt to slow down the ruck and said he would be speaking to referees' chief Bill Harrigan to define what is acceptable.
- AAP
