Waikato are three points behind but have two matches remaining, against North Harbour and Bay of Plenty.
Auckland's sixth loss from nine matches came via an error-strewn effort at a waterlogged Trafalgar Park, where they were outscored five tries to two.
Tasman dominated all facets to become the first team this season to win both games in a gruelling Wednesday-Sunday double.
Winger James Lowe and 19-year-old fullback Will Jordan defied the conditions with their speed and skill, having a hand in most of the tries.
Two early tries came through slick team moves, with halfback Billy Guyton crossing in his 50th appearance.
They led 19-6 at halftime, helped by a crucial tackle from Tasman back Trael Joass on his All Blacks Sevens team-mate Joe Ravouvou to deny the winger what seemed a certain try.
Jordan bagged his fifth try of the season after the break and lock Shannon Frizell responded to Auckland's opening try through Taleni Seu to virtually secure the result with a quarter to play.
- AAP