The two previously unbeaten teams in this year's National Provincial Championship took time to settle but Tasman opened the scoring with a try from Winger Timoci Tavatavanawai.
Campbell Parata later stretched the lead to 8-nil with a penalty kick.
It looked like Wellington full-back Ruben Love was going to cross the line with five minutes left in the first half but some desperate defence saw Tasman manage to hold him up.
Wellington finally got on the scoreboard when Jackson Garden-Bachop scored a penalty before the main break but Tasman led 8-3 at half-time.
Tjay Clarke scored Wellington's first try, which was then converted and the visitors trailed by just one.
Tasman found it hard to penetrate Wellington's wall-like defence but sheer persistence eventually saw Finlay Christie score Tasman's second try.
Riley Higgin's then replied with Wellington's second try and again the visitors were behind by just one.
But a brilliant try by local product Kyren Taumoefolau, which was then converted, stretched Tasman's lead to 23-15 with eight minutes left.
Tasman put the icing on the cake after a long build up was rewarded with a try from Nic Sauira.
Tasman Mako captain Quinten Strange had to go off with any injury early, but they benefited from the experience of All Black David Havili, who was released to play.
"It just shows how much it means to this region ...it's awesome to come back and play in front of our fans. I wanted to come down and try and defend it and be able to hold it today and really grateful for the opportunity," Havili said.
Wellington still sit at the top of the NPC table, but Tasman have a game in hand.
