The result at a rainy Stade de France saw the All Blacks become the first team to reach the final of a World Cup on five occasions.
"It's so sweet. It's new territory for this group," said player of the match Jordie Barrett.
"I am just so proud of this group. It's not done yet. We will have a very tough match regardless of who we have next week."
The three-time champions, who beat Ireland in a thrilling quarter-final last week, outscored Los Pumas by seven tries to none, mixing some doughty early defence with front-foot flamboyance in attack.
History was on New Zealand's side coming into the match, the All Blacks having won 33 of the 36 previous encounters between the two sides with Los Pumas claiming two victories, with one match drawn.
And although it was Emiliano Boffelli who opened the scoring for Argentina with a fifth-minute penalty, it was not long before New Zealand's dominance shone through.
The All Blacks spurned their first chance of a kick at goal, instead going to the corner for an attacking line-out and after a series of pick-and-drives, a long Richie Mo'unga cut-out pass found Jordan and the winger crossed for an easy try that the fly-half converted.
As forwards linked impeccably with backs, Jordan then turned provider, drawing in the final defender just enough to allow Jordie Barrett a line into the corner for New Zealand's second try.
Ragged Argentina
Although they pinched a couple of All Black line-outs, Los Pumas looked increasingly ragged around the breakdown and consistently lost territory through their ill-discipline at the ruck.
Boffelli grabbed his second penalty after a rare show of Argentinian pressure, but Juan Martin Gonzalez handed the advantage straight back after taking out Jordan under a high ball and Mo'unga slotted the penalty.
Mark Tele'a showed why All Blacks coach Ian Foster had recalled him in place of Leicester Fainga'anuku after serving a one-match suspension for a breach of team protocol, the winger jinking his way through four defenders towards the line.
The ball was worked left by Aaron Smith to find Frizzell unmarked on the wing, the outstanding flanker crossing for the All Blacks' third try.
Mo'unga's conversion came back off the post, but at 20-6 at half-time it felt as if the game was all but over as a contest.
That was confirmed just two minutes into the second period as Smith sniped over for a classic scrum-half's opportunistic try, Mo'unga kicking the extras.
A streaking break by the fly-half then set up the All Blacks deep in Argentine territory and with Tele'a proving a handful, Frizzell showed incredible strength to muscle his way over for his second try.
A raft of replacements disrupted the rhythm of the game, but Tele'a was on hand to draw in three defenders as New Zealand ran through the phases, leaving Finlay Christie to feed Jordan for his second five-pointer.
Scott Barrett saw yellow for needlessly playing the ball in a ruck, but Jordan was on hand to finish off his own chip-and-chase for a third try and his eighth at a single World Cup to draw level with Jonah Lomu, Julian Savea and Bryan Habana.
Argentina hung in there, however, and at least avoided the ignominy of suffering the highest margin of defeat in a World Cup semi-final, the All Blacks having beaten Wales 49-6 in 1987.
