Walker would then finish third in Race 1, around 0.99s behind Taupiri's Zac Fuller, with Sanson's Shane Miller in second, while Newton was back in fifth.
However, Newton would turn it around on Sunday – winning the second race after a restart with Walker only 0.071s behind him – while Paeroa's Blake Ross was third to follow up from his fourth placing on Saturday.
The third Gixxer race for the TT was an extended six-lap event, and this time Walker would be chasing no-one – winning with a 0.923s advantage from Fuller, with Ross third and Newton fourth.
Walker was happy with his performance throughout the weekend.
"The slipstream around the international track at Hampton Downs is just unbelievable," the 19-year-old said.
"There were people coming down to the straight in first, and they ended up in fifth.
"It took a bit of strategy."
In the third race, Walker was vowed and determined to get out to an early advantage to avoid the rapid lead changes that can happen in the bunched group, thereby putting the pressure on the rest of the field to catch up.
"They start tripping each other up and you're on the horizon."
Gixxer Cup is a development racing series for 14 to 21-year-olds on identical GSX-150F machines, which was started as an innovation for the 2017 Suzuki Series, but was then extended into a six-round event by being included in the 2018 superbike nationals.
Gixxer bikes are 154.9cc motorcycles with a top speed of about 140km/h, with competition rules stating they must be maintained to an identical standard.
As well as looking forward to Taupo, Walker is also making preparations for next season, as he is testing and developing a bike to enter the Pro Twin division.
In other results from Hampton Downs, Taupo's Scott Moir won the Superbike class, while Wellington's Sloan Frost did enough to maintain his healthy points lead.
The 600cc Supersport class was dominated by Christchurch's Jake Lewis with three straight wins, rocketing him to the top of the leader board.
The other New Zealand Superbike Championships class leaders after the weekend's third round are: Tauranga's Regan Phibbs (Supersport 300); Hamilton's Jordan Burley (650 Pro Twins); Christchurch's Nick Cain (250cc Production); Huia's Nathanael Diprose (Superlites); Rodney's Blayes Heaven (125GP); Auckland's Peter Goodwin and Kendal Dunlop (Sidecars).