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Canterbury were already assured of a first title since the 2016-17 season with two rounds to play in the competition, which dates back to 1906-07.
Canterbury dismissed Stags for 207 in their first innings and went on to score 391. The champions then reduced Stags to 299-5 before the match was called off at tea on the final day.
Canterbury also won the one-day Ford Trophy competition, while their women's team won the Super Smash and one-day Hallyburton Johnstone Shield, the first time one club has won four of New Zealand's five domestic titles.
The only trophy to elude them this season was the men's Super Smash, which was won by Wellington.