Abbott struck the winner 30 seconds from time after the Terriers came from behind to snatch the points.
But Town boss Jackson was ordered to the stands with 10 minutes left when he sparked a melee after clashing with City substitute Lee Johnson, son of manager Gary.
The ball went out of play near the Huddersfield bench and Jackson picked it up and refused to hand it back.
Johnson, making his debut as a substitute after signing from Hearts this week, pushed Jackson who then reacted by grabbing him by the throat and players from both sides rushed in.
City midfielder David Noble was booked for dissent while Jackson left the pitch side after being spoken to by referee Paul Taylor.
The two sides cancelled themselves out in a poor first half in which defences were on top.
Both sides are expected to mount a promotion challenge and the game only came to life in the second half.
City striker Phil Jevons, who grabbed a brace for Yeovil on his last visit to the Galpharm Stadium in April, scored his first goal for his new club just after the break.
Jevons first effort was blocked by Nathan Clarke but the ball came straight back to him and he stabbed it home.
At that point it looked like City would press home the advantage and Town had to be grateful to keeper Matt Glennon who brilliantly tipped Jevons' 20-yard shot onto the post.
That save allowed Huddersfield to stay in the game and striker Luke Beckett made it two in two games since his £85,000 switch from Sheffield United when he levelled in the 64th minute.
Gary Taylor-Fletcher played the final pass from a well-worked Huddersfield move and Beckett curled his drive inside the upright.
After the drama 10 minutes from time, the game was there for either side to win and Abbott, also on the scoresheet against Rotherham on Tuesday, grabbed the glory again.
A corner was only half-cleared and Abbott picked up the loose ball, turned and fired home despite Craig Woodman's desperate attempts to block it on the line.