The Tigers (22-5, 10-4 Southeastern Conference) made 12 of 14 free throws in the fourth quarter, but the two misses came in the final minute, giving the Lady Vols (21-6, 9-5) a chance.
Jordan Frericks fouled Rennia Davis on a 3-point attempt with 1.4 seconds left. Davis missed the first free throw and made the second before deliberately missing the third. Missouri got the rebound and iced the game on two Cunningham free throws with less than a second remaining.
Tennessee, down as many as 15 in the second quarter, took the lead with a 10-0 run early in the third. Missouri led by two entering the fourth quarter, and the Lady Vols tied it three times but never led.
The Lady Vols dropped their second straight game. They lost to Alabama 72-63 on Thursday night at home.
Frericks had 16 points for the Tigers, who shot 56 percent and were 19-for-22 from the foul line.
Jaime Nared led Tennessee — which had 14 offensive rebounds but hit just 11 of 16 free throws — with 25 points. Mercedes Russell added 10 points and nine rebounds.
Tennessee stays out on the road for its next game, a Thursday night contest at Florida, before closing out the regular season at home next Sunday against South Carolina.