The 22-year-old recovered from 2-0 and 5-3 down to prevail in Friday's first round of the World Series of Darts event at the Globox Arena, becoming the solitary Oceanic representative to progress to the quarter-finals.
Sherrock led from the outset, landing 94, 83 and 72 finishes to move to the cusp of victory, although she was denied a second win in August's treble-header after losing her range in the latter stages.
Milne rallied following a sluggish start - levelling at 2-2 with a 109 finish - and having survived a match dart at double 16 in a last-leg decider, he pinned the same target to complete a landmark win.
"I'm so happy," said Milne, who becomes only the third New Zealander in World Series history to triumph on home soil.
"Just to be playing on stage is an awesome experience for me. I never expected to win that game.
"I was definitely nervous early on, but the crowd were unbelievable. I cannot wait for tomorrow. I want to play again now!"
The 22-year-old will take on third seed Michael Smith in Saturday's quarter-finals, after the US Darts Masters champio battled past veteran New Zealander Warren Parry in a scrappy affair.
Smith continued his bid for a maiden World Series title Down Under with a 6-3 success, despite missing 22 darts at double.
Michael van Gerwen produced an impressive display on his return to New Zealand, as he began the defence of his NZ Darts Masters title with a 6-3 win against Bernie Smith.
The Dutchman defied three 180s and a brace of 12-darters from Smith to prevail with a 99 average, landing a magnificent ten-darter in leg seven, before completing the win with a clean 70 kill.
Van Gerwen now plays Jonny Clayton in a heavyweight last eight showdown, after the Welshman began his bid for back-to-back World Series titles with a crushing 6-1 win over Mal Cuming.
Clayton, last week's NSW Darts Masters winner in Wollongong, reeled off five consecutive legs to clinch a resounding victory, firing in an 11-darter in the penultimate leg to begin Friday's action in style.
However, Gerwyn Price produced the performance of the opening night in Hamilton, averaging 104.95 to overcome DPNZ number one Ben Robb in a high-quality affair.
World number one Price followed up a 14-dart break with a sensational ten-dart hold as he stormed into a 4-0 lead, yet Robb remained undeterred, producing a spirited fightback.
New Zealand's number one followed up 126 and 94 finishes with a 13-dart break to reduce the deficit to 5-3, only for Price to follow up his sixth 180 with a wonderful 124 finish to seal the deal in style.
Price will now meet fourth seed James Wade in a repeat of last weekend's NSW Darts Masters semi-finals, after the left-hander survived a match dart to edge out Gordon Mathers in a gripping last-leg shoot-out.
Wade, who trailed 4-1 at one stage, restored parity after eight legs of the contest with a sublime 145 checkout, before closing out a 16-dart hold on tops to triumph in a dramatic finale.
Elsewhere, top seed Dimitri Van den Bergh produced a stunning late surge to edge out Australian icon Simon Whitlock in the evening's finale, in a contest featuring nine maximums.
The pair traded four consecutive breaks in a topsy-turvy start, but with the scores locked at four apiece, Van den Bergh won the final two legs in just 23 darts to advance with a 100.37 average.
Despite back-to-back 180s from Whitlock to kick off the penultimate leg, Van den Bergh followed up an 11-dart break with a 123 finish on the bullseye to preserve his hopes of a third World Series title of 2022 in Hamilton.
The Belgian will face Joe Cullen for a spot in the semi-finals, after the Masters champion condemned Australia's number one Damon Heta to a third consecutive opening round exit Down Under.
Cullen converted a classy 120 combination in leg four to open up a 3-1 cushion, before wrapping up an emphatic 6-2 victory with a third maximum and an 11-darter.
The TAB New Zealand Darts Masters concludes with a blockbuster session on Saturday, featuring the quarter-finals, semi-finals and final in Hamilton.
Coverage will be available live on Sky Sport in New Zealand and through Fox Sports in Australia, as well as through the PDC's worldwide broadcast partners including DAZN and Viaplay.
Live coverage through PDCTV will be available in all worldwide territories outside of Germany, Austria & Switzerland (where coverage is exclusively via DAZN), while ITV4 coverage in the UK begins from 1630 BST.
2022 TAB New Zealand Darts Masters
Friday August 26
Jonny Clayton 6-1 Mal Cuming
Joe Cullen 6-2 Damon Heta
James Wade 6-5 Gordon Mathers
Kayden Milne 6-5 Fallon Sherrock
Michael Smith 6-3 Warren Parry
Michael van Gerwen 6-3 Bernie Smith
Gerwyn Price 6-3 Ben Robb
Dimitri Van den Bergh 6-4 Simon Whitlock
Saturday August 27 (1900 local time, 0800 BST)
Dimitri Van den Bergh v Joe Cullen
James Wade v Gerwyn Price
Michael van Gerwen v Jonny Clayton
Michael Smith v Kayden Milne
Best of 11 legs
Van den Bergh/Cullen v Wade/Price
Van Gerwen/Clayton v M Smith/Milne
Best of 13 legs
Best of 15 legs