Jorgenson scored 17 points and snared 14 rebounds while Hightower had 13 points and 12 rebounds before fouling out with 3:50 to play and Logan (22-and-3) ahead by nine.
Then she had to watch as King (21-and-3) almost erased what had been an 18-point lead at halftime. The Rangers survived a swarming attack by King, which had possession when down 50-47 with a minute to play.
But the Generals misfired on three attempts inside and the Rangers got two free throws by Michelle Mueller to make it 52-47 with seven seconds left.
King's Janelle Adams netted a 3-pointer with 1.7 seconds left for the game's final points.
Adams finished with 21 points and Sarina Adams had 13 for King. Brittney Brown had 11 rebounds and Simmons and Adams had 8 each.