Parsons' total included an old-fashioned, 3-point play to give the Lady Falcons a 32-31 lead after Crockett's Cassidy Rupert hit a shot at the buzzer to put the Lady Pioneers up 31-29 at the end of the third quarter.
"She was a warrior tonight, a real difference maker for our team," Volunteer coach Tracy Cloninger said. "She fought hard and rebounded the basketball. She ended with a double-double and she's had that capability all year."
Volunteer improved to 8-22 and will now face No. 3 seed Dobyns-Bennett on Wednesday night. The Lady Pioneers ended their season at 7-20 after getting outscored 17-8 in the final quarter.
"We came out flat and never recovered," Crockett coach Marty Story said. "They kept punching us in the mouth and we tried to withstand it, but there was lazy d, no help and poor rebounding. We did all the things you're not supposed to do."
Emma Gouge led Crockett with a game-high 16 points, but the next highest scorers were Bayleigh Day with six and Halle Scott with five.
Volunteer had more balance with 10 points for Kenady Knittle, eight from Chloe Salyer and seven from Atlee Dean. The Lady Falcons made the most of scoring opportunities, going 22 of 33 from the free-throw line.
"There are three things we try to win every game, the turnover-ratio, at the free-throw line and rebounds," Cloninger said. "We went 22 of 33 at the free-throw line and we get 35 rebounds so it was a good night."
It was closely contested throughout with the biggest margins at the end. Crockett led just 13-10 at the end of the first quarter, only to see the Lady Falcons claw their way back to a 22-20 halftime advantage.
After a long season, Cloninger talked about what it meant for the Lady Falcons' program to win in the district tournament.
"That's huge. It feels like everything wrong has happened to us," Cloninger said. "It seems like something has hung over the cylinder since the beginning of January. For us to see the shots fall and good things happen, it's huge momentum for us. No matter what happens Wednesday, it helps us go out on a high note for next year."
Cherokee 73, Volunteer 72
Ryan Bledsoe scored 27 points to lead the Chiefs (11-15) to the triple-overtime win over their Hawkins County rivals.
Bledsoe hit the game-saving and game-winning shots as Cherokee rallied from a seven-point deficit in the second overtime. Collin Trent scored 15 points and Bronson Shipley had 12 for the Chiefs.
Jacob Deal had 33 points for the Falcons, who trailed by 11 points early in the fourth quarter. Mason Reeves added 19 points as Volunteer finished its season 7-21.