Wellington seemed to have the chase in hand once experienced former international batsmen Michael Papps (45 off 28) and Hamish Marshall (36 off 20 balls) had the hosts at 73 in the seventh over.
Credit to Canterbury though, after scrapping back and taking four for seven in a 17-ball stretch. Legspinner Todd Astle grabbed a fine three for 18, including a spectacular one-handed return catch to remove Tom Blundell.
Wellington needed 10 off the last two overs, five off the last one, bowled by seamer Logan van Beek, and with a couple of crunching blows through the offside the ageless Luke Woodcock completed the job.
''It was touch and go for a while, with the way Toddy bowled," a chuffed Woodcock said.
''We just had to hold our nerve, take it as deep as we can and we were able to get over the line."
Wellington had lost their first four games in the competition, but won five of their last six. Defending champions Auckland, by contrast, won their first four, before losing their way.
CD had earlier secured their place in the final by finishing top of the round robin.