After enduring two extra time thrillers in earlier rounds, Napier progressed with three first half goals from Chris Greatholder, Andy Bevin and Miles John while a second half penalty from Angus Kilkolly completed the scoring.
In Auckland, five times winners Central United FC again did it the hard way before booking their quarter-final berth.
After earning their fourth round place with a fightback from 3-0 down with 10 men against Birkenhead, Central - playing at Kiwitea Street - claimed a 3-1 victory over fellow Northern Premier League outfit Glenfield Rovers, scoring twice late on despite playing the final 30 minutes down a man.
The visitors opened the scoring after just five minutes as Richard Beard gave Glenfield a flying start but Central recovered and restored parity three minutes before halftime through Emiliano Tade.
Junior All Whites defender Adam Mitchell earned an early shower with half an hour to go for a challenge on the edge of the Central penalty area but, despite the numerical disadvantage, the home side edged ahead in the 86th minute as Tade's deflected strike left All Whites goalkeeper Tamati Williams - who had earlier saved a Central spot kick - with no chance.
James Hoyt sealed the result with Central's third of the day four minutes into stoppage time.
On Sunday, Onehunga Sports returned from their trip to Tauranga City United with a 2-0 win, the visitors striking twice in the second half through Josh Ming and Sean Lovemore to advance while Melville United ended the cup run of Waikato Bay of Plenty Federation 1 League side Ngongotaha; Jevon Williams and Leon Newell scoring at Stembridge Road to see off the home side who got back to 1-1 three minutes into the second half through Dayne Willemsen.
Meanwhile, Hamilton Wanderers booked a fourth round trip to Bay Olympic next weekend after recovering from a 1-0 deficit to claim a 3-1 away win over North Shore United at Allen Hill Stadium on Sunday.
Edward Sillars gave the Northern Regional Division 1 side the lead in the rescheduled third round clash but a Mark Jones hat-trick turned things around for the Premier League outfit.
In the Southern Region, defending 2013 ASB Chatham Cup champions Cashmere Technical progressed to the last eight with a 1-0 win over Coastal Spirit at Linfield Park.
The victory was earned from the penalty spot in the 78th minute as Tom Schwarz struck the decisive blow.
Further south, Dunedin Technical - winners in 1999 - sealed their berth with an identical victory; substitute David Hayman settling the tie, also with a 78th minute winner, at the Caledonian Ground.
After a regional draw in the first four rounds, the competition draw for the quarter-finals will be done on a national basis.
