Cortez Ratima and Ardie Saves also scored tries for New Zealand while Rodrigo Isgro, Tomas Albornoz and Joaquin Oviedo went over for the home team.
The All Blacks' superiority showed through, although they had to see off a second-half surge from Argentina who were 31-10 down at the break but fought back to trail 31-24 before the All Blacks closed out the match.
The visitors were ahead after four minutes as Beauden Barrett set the tone with a penalty before Will Jordan's long pass sent Reece over in the corner to put New Zealand 10-0 up inside the opening 10 minutes.
Argentina quickly countered with a try of their own as a long pass out to right winger Isgro reduced the lead to three points.
New Zealand powered ahead with three tries before the break as Jordan sliced through from the halfway line to set up Ratima, followed by another try for Ardie Savea who powered over from a lineout drive.
There was still time for another New Zealand try before the break as their forwards hammered away at the try line before Ratima swung the ball out to Reece and he went over in the corner.
Argentina reduced the deficit 11 minutes into the second half as Albornoz attacked the line at pace and dived over as the All Black defence was caught napping.
When Billy Proctor was sent to the sin bin, there was renewed hope for the home side and they took advantage of their numerical superiority as Oviedo went over in the 64th minute to make the score 31-24.
New Zealand ended Argentine hopes of a recovery, however, as a lineout maul put Taukei'aho over and he added another try to seal the win.
The sides meet in Buenos Aires again next Saturday.
