With premier five-eighths Daniel Carter out of the tournament, his understudy, Colin Slade lasted 32 minutes until he left with a left thigh problem.
He was hurt early, stayed on for another 20 minutes but was replaced by squad rookie Aaron Cruden, whose right knee was heavily bandaged.
Inside a minute, Cruden was bloodied after he wore an arm across his mouth and nose as he slipped into a tackle.
Fullback Mils Muliaina's historic 100th test did not end well when he took a heavy hit in his ribs and failed to front after the interval.
Those dramas came as the All Blacks struggled to make an impression on their opponents.
They needed four penalty kicks from Piri Weepu to hold the halftime advantage as they were unable to beat the drifting Puma defence and their brutal tackling.
The All Blacks conceded a wonderful try to Puma loose forward Julio Cabello which gave his side the lead after half an hour of torrid action.
His No 8 colleague, Leonardo Senatore, broke past opposite Kieran Read from a scrum and 50m later, after a little fortune and some delightful interplay, Cabello crossed the chalk.
Meanwhile, the All Blacks bashed and searched but could not find a way through the scrambling defensive line.
There were numerous casualties in the heavyweight collisions, nothing drastic, but there were piles of aching limbs and tortured minds at the finish.
Midway through the second half, the All Blacks and most of the crowd thought Richie McCaw had planted the ball against the goalpost padding to claim a try.
Referee Nigel Owens was not so sure and television official Shaun Veldsman ruled no try. Weepu had to be content with his sixth straight penalty kick.
The All Blacks were making more inroads, buckling the Argentine scrum, clattering into contact, but still hunting an elusive try.
Longtime watchers were starting to talk about Don Clarke and his six penalty kicks to beat the Lions in 1959, until Read scored with 15 minutes left.
The ball squirted clear, Jerome Kaino flipped it past a would-be Argentine intercept and the All Black No 8 dived gratefully for the game-defining try.
Later, Brad Thorn galloped across for his first try of the tournament and Cruden converted from the sideline.
Next up are the Wallabies.
Henry's side lost their initial meeting with Deans' team in 2008 and their latest encounter in Brisbane in August. Between those bookend defeats, the All Blacks have lost just one other test against the Wallabies while picking up 11 victories.
The men in black get their chance to make it a dozen after escaping the Argentine clutches in the final World Cup quarter-final.
That leaves three New Zealand coaches - Henry, Deans and Warren Gatland (Wales) - supervising semifinal operations with French coach Marc Lievremont, who ends his association with the national team after this tournament.
Ireland, England, South Africa and Argentina will fill out their departure cards at immigration today after a rousing weekend of playoffs.
That leaves the cup tournament with a quartet of attacking thoroughbreds, four teams whose usual intent is to test their rivals' defensive sting by shifting possession rather than kicking it.
All Blacks 33 (K Read, B Thorn, tries; P Weepu 7 pen, A Cruden con.)
Argentina 10 (J Cabello try; F Contepomi con, M Bosch pen)
Half-time: 12-7
WHAT'S NEXT
Semifinal 1
France v Wales
Eden Park, 9pm Saturday
Semifinal 2
All Blacks v Australia
Eden Park, 9pm Sunday.
