Despite Alexandre Lacazette's third-minute opener, Arsenal laboured against the Terriers, who saw Steve Mounie's deflected shot pushed behind off the crossbar by Petr Cech early in the second half.
Ozil eased the tension by setting up Olivier Giroud – a half-time replacement for Lacazette, who sustained a groin injury that will rule him out of Saturday's clash with Manchester United – and Alexis Sanchez in successive minutes, before adding one of his own shortly after.
The Germany international's future at Emirates Stadium remains unclear with his contract set to expire at the end of the season and his effort has frequently been criticised, but Wenger was left in no doubt about his importance after his latest display.
"We started well but then we lost our focus and our passing and allowed them to come back into the game," the Arsenal boss told BBC Sport.
"Then we got the second goal and suddenly everyone played with more freedom and more technical quality - then Mesut Ozil showed what he can do."
Wenger added: "The last 20 minutes became comfortable but I would say Huddersfield did fight very well.
"In the second half I felt at some stages it could have been 1-1 but when we scored the second goal the game changed completely. We played very well, with freedom. We played a bit on the edge before that."
David Wagner rued Huddersfield's missed opportunities, with Collin Quaner failing to make the most of chances in each half, as the visitors fell to a third successive loss.
"Congratulations to Arsenal on the win - they deserved it," said Wagner.
"We had our best period, with two big chances, then they scored three in five minutes. They gave us a lesson in being clinical.
"We will be strong enough to leave this result - a harsh defeat - behind us quickly. The next game is just around the corner."