Canterbury made 188 for nine batting first with Janet Brehaut producing a steadying 53 after her side found themselves at 64 for the loss of four wickets.
Brehaut and Hayley Jensen, 33, put on 70 runs for the fifth wicket for the biggest partnership of the innings.
The Wellington bowlers, led by Sophie Devine, three for 33 and Sian Ruck, two for 25, put the clamps on once Brehaut and Jensen departed.
Wellington were the architects of their own demise.
At 47 for three by the 18th over, Devine and Emily Perry staged a 57-run partnership for the fourth wicket until Devine departed for 32.
A spate of run outs then demolished Wellington's innings beginning with Perry for 42.
Amanda Cooper was dismissed for a duck and Sian Ruck, six, Andrea Stockwell, three, Melinda Hodgson, 37 and Michelle Bunkall, nought were all run out as Wellington succumbed to the pressure of the chase, all out for 161 in 46.4 overs.
