They dominated territory and possession early on at Albany, using the full width of the field in opening out to a 26-0 lead after 24 minutes.
Halfback Bryn Hall was first across after five minutes, followed in quick time by the first of Li's five tries.
Fullback Shaun Stevenson added a third at the 18-minute mark, then Li crossed for his second as Harbour continued to stretch Taranaki's disorganised defence.
The visitors finally responded in the 26th minute, Declan O'Donnell hitting the inside ball at pace to slice through, with young No.10 Ciarahn Matoe adding the extras.
Li completed his hat-trick soon after with a runaway intercept off a Taranaki turnover and Harbour looked comfortable at 33-7 ahead with half-time looming.
But Taranaki crossed twice in five minutes, first through prop Jared Proffit off a Charlie Ngatai break, then via Matoe from winger Jackson Ormond's scything run down the left touch.
Ahead 33-19 at half-time, Harbour extended their lead 10 minutes after the restart, winger Matt Duffie finishing out wide and Li adding his fourth of the day before skipper James Parsons touched down from a lineout drive.
Taranaki worked hard to stay in touch, flanker Adrian Wyrill scoring from the pick and go, and Matoe grabbing a second with 10 minutes remaining.
But Harbour's defensive pressure was relentless, and they finished strongly with Matt Vaega scoring from an intercept and Li topping off a superb game with his fifth right on full-time.
North Harbour will travel to Christchurch for their semi-final against Canterbury next week, while Taranaki will host fourth-placed Tasman.
- NZN
