The Magpies moved four points clear of the relegation zone with a dominant performance against the Premier League's bottom club, who were reduced to 10 men when Tommy Smith was sent off after 20 minutes.
Almiron and Salomon Rondon had already hit the post by that point and Newcastle were in complete control thereafter at St James' Park.
The hosts registered 29 shots and finally broke the deadlock 59 seconds after half-time through Rondon and Ayoze Perez soon made sure of the points with a volleyed effort in which Almiron was involved.
Almiron had three shots on target and played six key passes before receiving a standing ovation from the crowd when he was withdrawn in the 81st minute in his first Premier League start since his record move from Atlatna United.
Speaking to Sky Sports, Benitez said of Almiron: "He did what we expected of him. He linked well with the other forwards. It was a great day for him and the fans.
"We did well so I was pleased with the performance of the players. It was difficult for them with 10 men but they still had chances. We had a lot of chances and we hit the post or bar three or four times."
Almiron told Sky Sports of his first appearance at St James' Park: "I'm very happy for the debut, even more for the three points, most important is the environment, I really enjoy it.
"Shame I couldn't score, it was a great chance [when he hit the post]. Most important is the win, we needed it. The goals will come."
It was another chastening experience for Huddersfield boss Jan Siewert, who has lost all four matches since replacing David Wagner last month and has the daunting task of leading the Terriers - who are 14 points adrift of safety - to survival.
"The red card broke our neck. Before we had chances and possession but the red card broke our neck," Siewert told Sky Sports.
"It was a diagonal ball from which they scored and when you have one man less it's very difficult. We spoke about the game and the situation changed the game. We will go on."