Jordie Barrett set up the winner on Saturday with a line break in front of the posts, before passing back inside to McAlister who slid over the line in front of delighted home fans at Waikato Stadium.
"To debut here, it's pretty awesome and I'm pretty proud to put the black jersey on and get to work with the brothers," said the Chiefs hooker.
"It's been quite a journey (for me), a lot of setbacks, a lot of resilience."
With his brother Scott and Beauden out with injuries, Barrett represented the family with distinction off the bench.
He made a try-saving tackle near the hour mark to hold off the valiant French, who battled in vain to break a win drought in New Zealand dating back to Dunedin in 2009.
Though France arrived in the country without a slew of their top players, they were a handful for Scott Robertson's All Blacks, barring the 43-17 second Test drubbing in Wellington.
Robertson fielded a much-changed line-up in Hamilton and was forced into a late shuffle when No.8 Luke Jacobson broke down in the warm-up.
He made way for Du'Plessis Kirifi who celebrated his first All Blacks start with a try near the hour mark that nosed his team in front after trailing 19-17 at halftime.
Les Bleus had made a bright start with scrumhalf Nolann Le Garrec first to cross over with a quick dash from the back of a maul in the eighth minute.
The French stretched the lead with a penalty before New Zealand responded when Will Jordan gathered a kick and sliced through for a 22nd-minute try.
France flyhalf Antoine Hastoy kept the scoreboard ticking over with a drop goal, while Le Garrec stretched the lead to 19-10 with back-to-back penalty goals.
But veteran All Blacks centre Anton Lienert-Brown, making a return from injury, pegged the French back nearly three minutes after the halftime siren with a hard-earned try on the back of 18 phases.
The French were unlocked again on 58 minutes by a Damian McKenzie grubber to the corner.
France fullback Leo Barre retrieved the ball over the line but winger Sevu Reece pounced on him to spill it clear, allowing Kirifi to score his first Test try.
Having taken the lead, the All Blacks ramped up the pressure and the brilliant Barrett broke through to set up McAlister's winner.
