It was the latest in a series of offences by the Pumas and referee Nigel Owens could have penalised them more for it.
It took until well after halftime for the All Blacks to begin to dominate. Captain Richie McCaw had a try ruled out by the TMO when he dived through a ruck after concerted pressure and almost touched a post.
While Henry will have been nervous throughout, one bright spot was the poise of Slade's replacement Aaron Cruden.
He went close to scoring in the right corner following a kick pass and went on several good runs, though if anything he could have looked to pass a little more when in space.
He also had the good fortune of playing outside Piri Weepu who is coming into the form of his life.
Aside from kicking 21 points, Weepu ran the show in the first half when things were looking very shaky. Slade had injured his ankle after about 18 minutes and took a limited part in proceedings until being substituted a quarter of an hour later.
But just when Weepu could be excused for going into his shell as the Pumas poured on the pressure, he went the other way, jinking and stepping and creating that little bit of inspiration the All Blacks were crying out for.
Weepu's fourth penalty of the half eased All Blacks into a slightly more comfortable position after the shock of Julio Farias Cabello's try.
That came after several embarrassing defensive lapses from the All Blacks. No8 Leonardo Senatore was the instigator, charging off the back of a scrum near halfway, easily stepping inside Kieran Read and created merry havoc as he surged into the All Blacks 22m before blindside flanker Cabello dived through a weak Sonny Bill Williams tackle attempt in the corner.
Contepomi converted from the sideline and thoughts were quickly returning to Cardiff.
The All Blacks desperately needed Weepu's contribution on the scoreboard because they just couldn't get things going on attack. The width game only works when on the front foot and the Pumas forwards were experts at slowing the ball down.
The edge the All Blacks forwards showed against Canada in their final pool game last weekend wasn't there. Kaino looked troubled by injury and Read looked rusty.
McCaw tried hard, as ever, but the lack of fluency in this department is a concern.
The Pumas could easily have gone to the break ahead rather than 12-7 down. Contempomi missed a relatively easy penalty attempt and Santiago Fernandez only just missed with an ugly drop goal attempt which remarkably went just under the crossbar and required a TMO decision to rule out.
Brad Thorn had the final say for the All Blacks when scoring a popular try with only minutes left. If the All Blacks wanted a tough test going in their semi-final, they certainly got it tonight.
New Zealand 33 (Kieran Read, Brad Thorn tries; Piri Weepu 7 penalties, Aaron Cruden conversion), Argentina 10 (Julio Farias Cabello try; Felipe Contepomi conversion, Marcelo Bosch penalty). HT: 12-7.
MATCH RECAP
