Cocksedge scored two of Canterbury’s 11 tries, and converted seven, for a haul of 24 points.
The work behind the pack from Cocksedge enabled Canterbury to control the game, while its tight five lurked with intent around the fringes and exposed weaknesses in a Spirit side suffering from a high turnover rate.
Canterbury’s potent back three of fullback Olivia McGoverne and wings Chelsey Smart and Becky Davidson all scored inside the first 20 minutes.
Then, as the Spirit appeared to be clawing its way back following the first of three Greer Muir tries, the Canterbury forward pack cut loose.
Its tight five dominated in the battle for the ball with prop Phillipa Love crossing for two tries against her old side, to assist Canterbury to a commanding 29-7 lead at the break.
Black Fern Stephanie Te Ohaere-Fox scored for Canterbury in the opening minute of the second spell.
And from the restart Cocksedge scored the first of two spectacular tries, after centre Elizabeth Pera ran the ball up, went wide, and, surrounded by Spirit defenders back-flipped an off-load to McGoverne, who then passed inside to Cocksedge, who sprinted from 40m out for the try.
With the clock running down, Cocksedge turned on another display of exceptional skills.
Taking the ball from a restart, she flat-footed the Spirit defence with a 60m run for a cracking individual try.
It came too late, but the Spirit side began to play to some of its potential, with late tries to Muir and Georgia Mason.
Otago coach Duncan McEwan said it would be back to basics for his side.
"We got beaten by a pretty good side," he said afterwards.
"We played intense, we played hard, but we weren’t playing smart."
An encouraging feature for McEwan was how the lineout functioned with captain and No8 Angie Sisifa, and locks Julia Gorinski and Annemieke van Vliet, in her debut game for the Spirit, proving influential.
In the midfield, Greer Muir gave the Canterbury defence plenty to think about.
The game marked a successful return to rugby for inside back Hannah Stolba, and her debut game for the Spirit.
Just 12 weeks ago, Stolba was nursing a broken ankle, but on Saturday, showed little sign of any discomfort, contributing some deft touches.
Farah Palmer Cup
The scores
Canterbury 69
Phillipa Love 2, Kendra Cocksedge 2, Chelsey Smart 2, Becky Davidson, Olivia McGoverne, Stephanie Te Ohaere-Fox, Sam Curtis, Keilamarita Pouri-Lane; Cocksedge 7 con)
Otago Spirit 24
Greer Muir 3, Georgia Mason tries; Megan Manson 2 con
Halftime: Canterbury 29-7