Southland's No 11 Jaye Thompson had a busy afternoon, fielding an array of high balls and grubbers, but in truth, Harbour needed to better employ a skid kicking game in these conditions.
Right wing Matt Duffie showed his skill under the high ball and set up Li for his second try. First five Bryn Gatland was flawless off the tee, helping to keep Harbour's nose in front.
Once again Harbour were frustratingly profligate with possession, though the wet conditions were a hindrance. But they did score three second half tries, two of which were opportunistic. Li's first half try came from a Gatland-Matt McGahan switch, while lock Gerard Cowley-Tuioti ripped the ball free from a maul after a Stags' snafu just out from their line, while skipper Chris Vui dived over from close range to solidify some powerful work off the bench from loose forward Hapakuki Moala-Liava'a. They could have scored two more tries if all had gone to plan.
Stags prop Peni Ravai caused some consternation when he burst through to peg the margin back to 23-14, until Harbour's late flourish.
They hold fourth position, dependent on the outcome of the Steamers-Auckland game.
North Harbour are back at home on Saturday afternoon facing the Steamers, while Southland are in Wellington on Friday night.
North Harbour 35 (Tevita Li 2, Gerard Cowley-Tuioti, Chris Vui tries; Bryn Gatland 2 con, 3 pen, Matt McGahan con)
Southland 14 (Peni Ravai try; Wharenui Hawera 3 pen)
HT: 16-9