Moir qualified fastest in the F1 class and he finished the day at Manfeild as overall runner-up, with his carding of second and fourth in the two races enough to give him a one-point edge over Richardson for the day's tally.
Richardson finished fourth and second in his two F1 outings on Sunday, equal to Moir's race results, but Moir's extra point for setting the fastest qualifying time gave him the welcome boost.
Richardson's series lead has suffered only minimal damage, having been leading by four points coming into the round.
Hickman, on the other hand, made gigantic advances after his Kiwi debut at Taupo.
"It wasn't all doom and gloom at Taupo, but I think this [Manfeild] circuit better suited the bike than the track at Taupo did," said the 31-year-old from Lincolnshire.
"The level of talent here in New Zealand is actually quite good. It definitely wasn't easy to win today."
There is only a little bit of respite before the third and final round, the traditional public street race spectacular on Boxing Day, the bikes on that once-a-year occasion being raced around Whanganui's iconic Cemetery Circuit.
Despite being a first-time visitor to New Zealand, Hickman is obviously a quick learner and the curbs, tight bends, railway crossings and slick painted road markings at Whanganui should present no problems for the 2018 Isle of Man winner.
"It's my first time in New Zealand, but it has all been good," Hickman said.
"We only got to the Taupo track the day before the racing there. I only landed Friday morning and I was racing there Saturday and Sunday, so I was sort of thrown in at the deep end, but I still really enjoyed it.
"I didn't have any jet lag at Manfeild and had an extra day riding here, so I went better there.
"On my way to Manfeild I stopped off in Whanganui and did a couple of laps [of the Cemetery Circuit] in the car.
"I knew it was a short circuit, but I didn't think it was so wide.
Hickman seemed perhaps unaware that the Cemetery Circuit has never before been described as or considered by most racers as "wide".
"I think there are loads of passing opportunities, so I'm feeling confident for Boxing Day.
"Obviously, I'm not going to get a lot of time to practice on it, which makes things a little more tough, but we'll have some fun there and do some wheelies and skids. That's what it's all about."
Meanwhile, there were changes near the top of several other classes also at Manfeild.
In the 600cc Formula Two class, Whakatane's Damon Rees was again unbeatable, while his nearest challenger, Rangiora's Avalon Biddle, dropped from the runner-up spot for the series after crashing while leading the second race on Sunday.
The new No2 rider in this class now is Rogan Chandler, with the Lower Hutt man finishing third and second in the two F2 races on Sunday and moving up from fourth overall in the series.
Chandler edged out Feilding's Ashton Hughes, who himself moved up from fifth overall to lock in third thanks to his fourth and third results at Manfeild.
Palmerston North's Jacob Stroud continues to lead the Formula Three clas, while Auckland's Scott Findlay still tops the Post Classics, Pre-89, Juniors class.
Te Awamutu's Gary Morgan remains in control of the Bears (non-Japanese bikes) and Formula Sport, Juniors class, and Tauranga's Duncan Hart continues to dominate the Super Motard class.
Visiting British rider John Holden, with Tauranga 'passenger' Robbie Shorter, are still unbeaten in the Formula One sidecars class.
Tauranga pair Barry Smith and Tracey Bryan are similarly running away with the Formula Two sidecars class, but there were changes at the top of several other categories.
Taupiri's Zak Fuller is the new leader in the Gixxer Cup class after Manfeild, while Paraparaumu's Peter Bogusz has taken over the lead in the Post Classics, Pre-89, Seniors.
Ngaruawahia's Steve Bridge is the new man in charge of the Bears (non-Japanese bikes) and Formula Sport, Seniors class.
Whanganui's Tarbon Walker managed to qualify his Formula Two bike in 11th place in the 25 bike field for his class in Manfeild, and had finishers of ninth and eighth in the two races, which was enough to come sixth overall for the round.
In the F1 Sidecars, Whanganui's Ian Staples and Mark Thompson qualified in eighth and had two finishers of sixth place in the races.
That was enough for third overall for the round and moves the pair into second place in the series heading into their home circuit in Whanganui.
Overall Points after Round 2.
Formula One superbikes: 1. Shane Richardson (Wainuiomata) 84 points; 2. Scott Moir (Taupo) 81; 3. Peter Hickman (UK) 36.
Formula Two 600: 1. Damon Rees (Whakatane) 102; 2. Rogan Chandler (Upper Hutt) 78; 3. Ashton Hughes (Feilding) 71.
Formula Three: 1. Jacob Stroud (Palmerston North) 102; 2. Leigh Tidman (Taumarunui) 84; 3. Richard Markham-Barrett (Nikau Valley) 74.
Gixxer Cup: 1=. Zak Fuller (Taupiri) and Jesse Stroud (Hamilton) 90; 3. Clark Fountain (Greymouth) 88.
Post Classics, Pre-89, Seniors: 1. Peter Bogusz (Paraparaumu) 89; 2. Gian Louie (Hastings) 87; 3, Duncan Coutts (Whangarei) 74.
Post Classics, Pre-89, Juniors: 1. Scott Findlay (Auckland) 98; 2. Dean Bentley (Lower Hutt) 90; 3. Chris Sales (Palmerston North) 62.
Bears (non-Japanese bikes) and Formula Sport, Seniors: 1. Steve Bridge (Ngaruawahia) 91; 2. Brendon Coad (Auckland) 89; 3. Malcolm Bielski (Wellington) 71.
Bears (non-Japanese bikes) and Formula Sport, Juniors: 1. Gary Morgan (Te Awamutu) 101; 2. Robert Lammas (Palmerston North) 86; 3. Paul Jenkins (Kaikohe) 72.
Super Motard: 1. Duncan Hart (Tauranga) 102; 2. Andrew Rudd (Ashburton) 80; 3=. Will Young (Wellington) and Russell Josiah (Taumarunui) 72.
F1 Sidecars: 1. John Holden, Robbie Shorter (England/Tauranga) 102; 2. Ian Staples, Mark Thompson (Whanganui) 78; 3=. Peter Goodwin (Albany), Louise Blythe (Whanganui) and Jarrad Winter, Kelly Winter (Christchurch) 62.
F2 Sidecars: 1. Barry Smith, Tracey Bryan (Tauranga) 102 points; 2. Gary Bryan, Philip Hyde (Leceister, UK) 88; 3. Mark Halls (Auckland), Darren Prentis (Taranaki) 80.
