The off-spinner drove the ground-breaking Australian bowling assault to reject the Kiwis for 136 and seal another overwhelming success over the Black Caps after comparable triumphs in Perth and Melbourne.
Australia have been magnificent this season, winning every one of the five Tests at home - two against Pakistan and three against New Zealand - subsequent to holding the Ashes by attracting the arrangement 2-2 England.
Australia announced their second innings at 217 for two with David Warner scoring an unbeaten century, leaving the Black Caps with a modified 416-run focus in the fourth innings on a wearing Sydney Cricket Ground pitch.
In any case, the Kiwis clasped under the weight of Australia's unrivaled bowling assault with Mitchell Starc taking three for 25 to help the wiles of spinner Lyon.
New Zealand were reeling right on time at 27-4 and never recouped after Starc and Lyon took two wickets each in the center session to put the slides under the voyagers.
Starc expelled the two openers, Tom Latham and Tom Blundell, in the initial five overs.
Blundell tumbled to a shocking catch by a plunging Lyon at point for two and remain in captain Latham lost a survey for leg before wicket on umpire's call for one of every a breaking hit to New Zealand's expectations.
Jeet Raval was out in a survey to the faintest of edges on 'Snicko' in Lyon's first over for 12, with the Kiwi innings disentangling under the invasion from the Australian assault.
First-innings top-scorer Glenn Phillips went for a duck after innovation identified a black out outside edge to wicketkeeper Tim Paine off Lyon leaving the Kiwis a precarious 22 for four.
Taylor's Kiwi record
Ross Taylor turned into the main untouched Kiwi batsman, going past Stephen Fleming (7,172) preceding he was bowled by Pat Cummins for 22 to step through his Examination total to 7,174.
Large hitting Colin de Grandhomme smacked Lyon for six over additional spread to raise his fifty however went next ball hoicking to Joe Burns at profound mid-wicket to take an agreeable catch for 52.
Todd Astle was out to an eminent jumping get by James Pattinson in the outfield for 17 to give Lyon his fourth wicket of the innings late in the day.
Starc yorked William Somerville's center stump for seven and BJ Watling was the last to fall, got at in reverse square leg by Pat Cummins for 19.
Prior, Warner finished his 24th Test century with a clasp off his cushions for three goes through mid-wicket and stayed unbeaten when captain Paine announced upon the rejection of Marnus Labuschagne.
Labuschagne, who was dropped on four out of a guideline got and bowled chance by leg-spinner Astle, was gotten at long on off Matt Henry for 59 - his seventh score more than 50 of every eight innings this brilliant local summer.
Labuschagne completed the home five-Test season against Pakistan and New Zealand with a staggering total of 896 runs, made up of his 215 in the principal innings, three different hundreds of years and three half-hundreds of years in eight innings.
There was dramatization late in the innings with the Australians pursuing fast runs in front of the announcement when Warner was given an official admonition by umpire Aleem Dar for running down the center of the contribute hurrying a solitary.
It brought about five punishment runs being added to New Zealand's first innings absolute importance their objective was changed down from 421 to 416.
The Test was played against the background of one of Australia's most crushing bushfire seasons with in any event 24 individuals losing their lives in bursts seething the nation over, remembering for the edges of Sydney.