Abbott had already become the first player since George Brown in the 1920s to score in each of Town's opening five fixtures and quickly set about adding another.
The former Poland under-21 international, who scored 28 goals last season, easily beat keeper Dimitrios Konstantopoulous after being put through by Andy Holdsworth's superb 40-yard pass on 13 minutes.
Abbot could also have added to his tally more than once in a game the home side nearly lost thanks to a stunning revival by the visitors.
The striker blasted over from 18 yards after expertly controlling Chris Brandon's pass on 26 minutes and he could have sealed victory late on when put through by Nathan Clarke but Konstantopoulous this time parried his effort.
By this time Town were already two goals to the good with Danny Schofield capping an excellent move with a neat finish after 18 minutes.
Hartlepool were totally outplayed in the first half and it looked like the Terriers would stretch the unbeaten record to 14 games in a run that goes back to December last year.
But Hartlepool made a double substitution at half time that transformed the contest and left Town clinging on for victory.
Adam Boyd, who replaced Jon Daly after the break, cracked in a superb curling effort past keeper Paul Rachubka to reduce the arrears just five minutes after coming on.
Boyd, who has been subjected to allegations about his private life following a court case last week, put his off-field troubles behind him by nearly setting up a deserved equaliser for Richie Humphreys on 66 minutes.
Rachubka parried the veteran former Sheffield Wednesday midfielder's effort and was also equal to strikes from Michael Proctor and Michael Nelson as Hartlepool battered the home side without making a deserved breakthrough.
As Hartlepool pressed for an equaliser they left gaps at in the back which Abbott was able to exploit but he could not add to his earlier goal.