Former Poland Under-21 international Abbott struck in the last minute with a header that ensured Town remain undefeated at home in 2005.
Abbott headed substitute Andy Holdsworth's cross over Robins keeper Steve Phillips to extend the good run to12 games unbeaten at home since January.
And the hit man, who scored 26 league goals last season and was on target on the 2-1 defeat at Nottingham Forest on Saturday, could have had a hat-trick.
He hit the bar with a powerful long range effort on 24 minutes and planted a free header wide of the target after the break when it seemed easier to score from Danny Adams' perfect cross.
Abbott's performance outshone the uncharacteristically subdued displays from past and present Huddersfield legends Marcus Stewart and Andy Booth. Former Town legend Stewart, who had a four year spell at Huddersfield before a controversial £2.5million move to Ipswich, was marked out of the game.
And Booth, who has scored 110 goals for his home town club in two separate spells, had a generally below-par match. The closest he came to scoring was with a header from an Adams corner in the first half that was cleared off the line.
The home side dominated the opening period and created a hat full of chances that should have seen them take the lead before half-time. And their fluency in the second half was disrupted when the outstanding David Mirfin was stretchered off with a suspected hamstring injury.
City held their own and had opportunities to take the lead against the run of play. David Cotterill fired wide on 20 minutes and Luke Wilkshire, later sent off for a second bookable offence, fired straight at Town keeper Paul Rachubka nine minutes later after a run from deep.
But Mirfin's injury ultimately proved fortuitous as it was his replacement, Holdsworth, who beat two challenges down the right to fire over the cross that allowed Abbott to steal the points for Huddersfield.