"We went man-to-man on the out of bounds play because if you play zone, then a 3-point shot will beat you," said Kennedy, who watched Tennessee's Josh Richardson miss a potential game-tying basket from 12 feet and Ole Miss survived.
"I just didn't want to see him (Richardson) hit a 3. He made a great play to get a clean look and he got a good shot. We got a kind bounce," Kennedy said. "Our margin of error is awfully small and we've proved that for 27 games."
The win was the eighth in the last nine starts for the Rebels (19-8, 10-4), who remained tied for third place in the SEC standings. Ole Miss has won five of the last six games decided by six points or less and strengthened its case for an NCAA Tournament berth.
Stefan Moody led the Rebels with 22 points, including six from 3-point range and added six steals. Jarvis Summers had 13 points, eight assists and combined with Moody to hit three free throws in the final two minutes for the win.
"We're a confident team right now and we're having fun," Moody said.
"We've still got things we want to accomplish and we are still working to get to where we want to be."
The loss was the latest in a series of tough-luck decisions for the Volunteers (14-12, 6-8), who have lost five of the last six games.
Tennessee is 2-5 in the SEC in games decided by six points or less.l
Richardson missed a difficult go-ahead 3-point shot with 6 seconds left before Tennessee got the rebound and called a timeout. Richardson made a nifty move after making an inbounds pass with 4.8 seconds left, but a clean shot rattled the rim and fell out.
"Our best player had the ball in his hands twice in the last 15 seconds. So I have no problem at all with the shots. Josh has hit big shots all year," Tennessee coach Donnie Tyndall said. "Tonight it was unfortunate that it didn't go in."
Ole Miss finished 21 of 54 (38.9 percent), including 11 of 31 from 3-point range. The Rebels, ranked second in the nation in free throw percentage at 78.6 percent, managed only 6 of 10 from the line.
Tennessee was 22 of 51 (43.1 percent) from the field and 9 of 23 from behind the 3-point line. Punter and Richardson accounted for seven of the 3-pointers, including 4 of 8 from Punter. The Vols led 30-27 at halftime and led by as many as eight points, 44-36 with 13 minutes remaining.
Moody led a 19-6 surge by the Rebels, highlighted by 11 points, that gave Ole Miss a 52-47 lead with 7:57 left. Tennessee regained the lead on Moore's free throw, 57-56 with 3:07 left, setting up the decisive free throws and defensive stand by the Rebels.
"Give Tennessee a lot of credit for getting us to play at their pace and making tough shots," Kennedy said. "But we're satisfied to survive this with a win."
Tennessee: Armani Moore finished with 15 points, but added a game-high 9 rebounds, 5 assists, 2 steals and 2 blocked shots. In the SEC, The Vols are 2-5 in games decided by six points or less.
Ole Miss: The Rebels have won 36 games over SEC foes in the past three seasons, trailing only Kentucky and Florida. Jarvis Summers finished with eight assists and has 67 assists in the last 10 games. Over the past three seasons, Ole Miss is 4-1 against Tennessee.
Ole Miss hosts Georgia Wednesday.
Tennessee hosts Vanderbilt Thursday.
AP: Ole Miss 59, Tennessee 57
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