The Lady Trojans jumped out to a 3-0 lead in the bottom of the first inning. Canaan Burnett drove in a run with a single and Madison Collier later ripped a single to score two more runs.
They added their final run in the bottom of the fourth as Faith Alexander plated a run on a fielder's choice.
The Lady Generals (0-1) threatened in the top of the third, but GLMS catcher Karsan Gazaway helped her team escape trouble by throwing out two runners at second base.
Heritage would load the bases in the fifth, but scored only once on an RBI-single by Reagan Norfleet. Alexander made a great throw from deep in the hole at shortstop to Gazaway at home, forcing a runner for out two, then catching a shallow leftfield flyball to end the inning.
The Lady Generals would make things interesting in the top of the seventh, loading the bases again with just one out. Gordon Lee would get a force out at the plate, but a fielding error would plate two runs and put the tying run at third.
But Burnett, who went the distance to get the win, would induce an infield pop-up to Alexander to end the game.
Burnett also improved her record to 2-0 by allowing four hits and three walks with six strikeouts. Maddie Morris took the loss for Heritage.
Both teams are scheduled to take part in a tournament at the Jack Mattox Complex in Ringgold this weekend. Heritage will play their first game at 5 p.m. versus North Whitfield, while Gordon Lee will take the field at 6:30 against Calhoun.