But the home side could keep the high-flying Makos at bay for only so long, with moments of individual brilliance turning the match and periods of pressure eventually breaking Wellington's resolve.
Tasman scored 30 unanswered points in as many minutes as they overturned a 12-6 second-half deficit, with their sudden attacking spark overwhelming a Wellington side who were good value for their early advantage.
The home side shaded an opening half that featured the type of rugby perhaps expected from two teams without a loss between them, with enterprising attack scuppered by excellent defence.
The only man able to break free from the shackles was Wellington flanker Vaea Fifita, taking another large stride in his breakout campaign and laying on Wellington's opening try for Frae Wilson.
But that was as good as it got for the hosts, who turned over the ball far too often and were made to pay for their errors by a rampant opposition.
Wellington 17 (Wilson, Garden-Bachop, Goosen tries; Bentley con)
Tasman 36 (Samu, Fonotia, Kotze, Christie tries; Banks 2 pens, 2 cons, Havili 2 pens)
HT: 6-5