Todd Astle took 3-44 for the visitors in an influential spell, while Andy Ellis (1-43 from nine overs) and Kyle Jamieson (1-33 from nine overs) kept Auckland's scoring rate in check with economical offerings.
Canterbury decided to take an attacking approach in their response, with openers Tom Latham and Ronnie Hira playing aggressively to begin the chase.
Hira made 31 from 33 balls to kick-start the innings, while Latham struck a 50-ball 42 before being trapped in front by Tarun Nethula.
Although Grobbelaar slowed the flow of runs by going for just 15 from his opening spell of five overs, recent Black Caps debutant Henry Nicholls proved potent, marking his return back to domestic cricket with a valuable 56.
Nicholls was the third wicket to fall with 63 further runs needed, and Peter Fulton took control from there, blasting four sixes in a 55-ball 65 as Canterbury eventually cruised to victory with 12 overs remaining.
Canterbury have now won four of their five games, with the other being rained out, while Auckland picked up their second loss of the campaign.
Two games are scheduled for tomorrow, with the Northern Knights hosting the Otago Volts in Whangarei, while Ben Wheeler and Doug Bracewell will return for the Central Stags when they take on the Wellington Firebirds in Palmerston North.
