Abraham helped Swansea take a lead into halftime after he pounced on a defensive mistake from Huddersfield goalkeeper Jonas Lossl in the 42nd minute.
He then gave Swansea a buffer on the other side of halftime when he poked home Jordan Ayew's shot in the 48th minute.
After the game, Abraham summed up his performance by saying: "I was brought here to score goals and that's what I really want to do."
Swansea coach Paul Clement was full of praise for Abraham at the post-match conference.
He said: "That was the best game Tammy has played, I was pleased with his overall performance.
"He was threatening the defence with his runs, his play with his back to goal was better and he put in a good shift defensively."
Watch the highlights of the match below, courtesy of Swansea City:
This was Swansea's first home win of the Premier League season. They will be hoping to replicate this result on October 21st when they take on Leicester at home.