Summer signing Cadamarteri went down with a hamstring injury on the eve of the campaign and only returned as a substitute at Northampton last week.
Luke Beckett gave the home side the lead in the 36th minute with his first goal in seven games and Cadamarteri sealed it on the hour.
Forty-five seconds into the second half Luton had five-goal top scorer Paul Furlong sent off for a second bookable offence.
It was a bruising encounter in which Huddersfield midfielder Andy Holdsworth took the brunt of the challenges.
But, despite that, he turned in a man of the match display.
Huddersfield also gave a debut to on-loan midfielder Ronnie Wallwork - the West Brom player who has not played in the league since he was stabbed in a Manchester nightclub last November.
He brought a calming influence and managed to last the full 90 minutes.
Beckett and Cadamarteri had early chances before Beckett gave Huddersfield the lead.
A clearance from keeper Matt Glennon was headed on by Beckett and Cadamarteri went in with debutant keeper Ben Alnwick and the ball broke for Beckett who waited before firing home.
Furlong was booked for a foul around the time of the goal and saw red just after the restart when he appeared to elbow Richard Keogh as they jumped for a header.
Cadamarteri sealed the points when he was brilliantly set up by Holdsworth, whose run and cross left the striker unmarked.
Huddersfield made the extra man count as the game wore on and Chris Brandon had a powerful shot beaten out by Alnwick and Holdsworth should have wrapped it up when he side-footed wide with 10 minutes left.