The Cherokees entered Monday's contest at Tennessee School for the Deaf with a 3-17 record and needing a victory to avoid a last-place finish in the district.
Greenback's nearly two-month drought came to an end as they left TSD with a 73-56 win.
Senior Eric Anderson gave the team an early boost, hitting five shots, four from beyond the arc, in the first quarter for all of his 14 points.
Junior Josh Pace, who finished with a team-high 15, hit four times from long range as well, twice in the second quarter and twice in the fourth.
Greenback took a 38-23 lead into the half but did not keep up their level of play in the third, allowing TSD to win the quarter 22-13 and close the gap to just six.
The Cherokees responded well in the fourth, scoring 22 and pushing back into a double-digit lead. The team now turns its attention to Friday night’s tournament opener against Rockwood, which is 18-7.
Rockwood won both regular season meetings with the Cherokees, taking the first game 48-26 and the second 54-35. Friday’s game will be played at 7 p.m. at Rockwood.
Greenback's girls, who did not play Monday, begin the district tournament at 7 p.m. Thursday at Harriman. The Lady Cherokees split the season series with Lady Blue Devils, winning 52-50 and losing 41-36.