COLUMBIA, Mo. (AP)-- A day after his cousin died of a gunshot wound in Kansas City, Marcus Denmon understandably hit the court in a funk.
By the end, the junior guard made the biggest play that kept Missouri's homecourt winning streak alive at 51 straight.
Denmon scored all but two of his 21 points after halftime and made a three-point play off his steal and layup with 5.8 seconds to go in overtime as the Tigers (No. 11 ESPN/USA Today, No. 15 AP) held off Vanderbilt 85-82 on Wednesday night.
"The first half he played with a heavy heart, he lost a family member," coach Mike Anderson said. "In the second half he was the big-time leader."
Missouri (7-1) entered with 43 straight non-conference home wins with an average margin of 26 points under Anderson, in his fifth season.
"At home, you want to come out with a comfortable win," said guard Michael Dixon, who had 15 points and hit a layup that tied it at 82 with 33 seconds to go. "This was far from comfortable."
Ricardo Ratliffe added 14 points and nine rebounds for Missouri.
On the deciding play, Denmon deflected a pass toward the Missouri basket, retrieved the ball in plenty of time for a layup while being fouled by Brad Tinsley, then added the free throw.
"There's really no excuse for how that all unfolded," Vanderbilt coach Kevin Stallings said. "Nevertheless, we had our chances. We could have salted the game away with some free throw makes."
Marcus Denmon and Marion Denmon, 20, grew up in the same house. Dixon, also from Kansas City, had been a close friend of Marion Denmon.
"It's been a long couple days. People have been real emotional and stuff," Dixon said. "[Marcus] came out and played his heart out. That flowed through the team."
John Jenkins had 23 points and five 3-pointers for Vanderbilt (7-2), which had won five straight. Tinsley missed on long 3-point attempts at the end of regulation and at the buzzer in overtime.
"I think when you're in a game like this, when you walk away from it you feel like you should have won," Stallings said. "If they had lost they would have felt like they should have won."
Jeffery Taylor added 18 points and 10 rebounds and Festus Ezeli had 16 points, nine rebounds and six blocked shots in the Commodores' first road game of the season. Vanderbilt is a bit shorthanded with guard Andre Walker sidelined with mononucleosis but did a good job against Missouri's all-court pressure even though Taylor played 43 minutes and Jenkins 41.
Denmon was 1 for 8 early in the second half, then went 6 for 11 the rest of the way as Missouri improved to 4-0 at home this season.
Missouri was held to a season-worst 38 percent shooting from the field. Vanderbilt has yet to allow an opponent to shoot 50 percent, but hurt itself by going only 11 for 22 from the free throw line including 4 for 10 by Ezeli.
Vanderbilt hit 76 percent at the line its first eight games.
Ratliffe hit the second of two free throws with 6.6 seconds left to tie it at 72 and force overtime.
Jenkins bounced back from a 10-point effort on 1-for-7 shooting against Belmont with his fourth 20-point game out of five.
"I was feeling it in warmups," Jenkins said. "I just knew if I came out there and found my spots, I'd make the shots."
Vanderbilt's 54-48 lead with 13 minutes to go was the biggest for either team after Missouri's early 16-9 lead.
Dixon had seven points in the final 2½ minutes of the first half, capped by a driving layup just before the buzzer to give Missouri a 40-37 lead.