The visitors went 1-0 up on the half hour with David O'Sullivan scoring.
Harps had a chance to equalise from the penalty spot when Pat McCann was brought down in the area.
The resulting penalty taken by Sean McCarron was saved by the Longford keeper Chris Bennion.
Mark Salmon wrapped up the game eight minutes from time to give the champions their eighteenth win of the season.
Harps ended the year fifth 28 points off the winners.
Afterwards, Ollie Horgan gave his reaction.