Great Britain's Olympian Geraint Thomas finished third for Team Sky, behind Movistar's Spanish rider Javier Moreno, as he recovered from Friday's setback with a well-judged performance in the intermediate sprints on the final stage.
Team Sky lifted Thomas to the front in the first sprint after eight laps for a three-second time bonus and he picked up one more with third place at the second, after 12 laps.
After that, Lotto Belisol controlled the stage as Greipel was first to the tape yet again, edging out Australian Mark Renshaw with Sky's Edvald Boasson Hagen third and Thomas sixth. It was Greipel's 100th career stage win and his 14th at the Tour Down under.
Slagter, though, had gone into the day with a commanding 13-second lead and his overall win was never in doubt.
It was a major boost for the team which formerly raced under the Rabobank name before the Dutch firm withdrew their sponsorship in response to cycling's doping scandals.
Slagter, the first Dutch winner of this event, said: "The team has been doing really well and I'm proud to show this team to the world."
Team Sky rider Bernhard Eisel was delighted the team were able to deliver Thomas back onto the podium after he dropped to fifth on Friday.
He said: "It was perfect teamwork today [Saturday]. It was hard work, I can't even talk - I literally turned myself inside out today.
"It was really important, Geraint yesterday [Friday] gave everything.
"We hadn't done anything wrong yesterday, Slagter was just stronger and Simon Gerrans as well. We fought back today and I'm happy for everyone in the team."
Boasson Hagen added: "It was great to get 'G' on the podium, and a nice podium finish for me (today) as well."