Watson, who didn't start because of a strained right hamstring sustained Thursday, had 16 points, 10 rebounds and three blocks. His dunk turned into a three-point play with 4:10 left that gave Virginia the lead.
"It was amazing that Travis played," Virginia coach Pete Gillen said. "That he had such a good game with 16 and 10 ... I'm speechless."
Virginia (13-3) finished the game on a 17-3 run started by Watson, turning a tight duel into a runaway that had University Hall delirious
"They got juiced up when we got the lead," Gillen said of the crowd. "That got them a little bit unnerved, I think, and helped re-energize us."
The Cavaliers, flat for much of the game, also helped themselves by making 34-of-41 free throws, including 18-of-21 in the second half, by outrebounding the Tigers 42-33 and holding them to 43.3 percent shooting.
And, Gillen said, when the team does what it's supposed to do.
"If you defend and you rebound, you're going to be in a lot of games," he said. "I think we did a pretty good defensive job for us, and we rebounded well and made our free throws. It was a great victory."
The end came quickly after Watson's move down the lane gave the Cavaliers a 71-69 lead. Donald Hand followed with a free throw, Wesley Stokes missed the front nd of a one-and-one for the Tigers and Chris Williams hit a pair from the line to push Virginia's edge to 74-69.
When Kareem Rush also missed the front end of a one-and-one for Missouri (12-5) with 2:09 left, Williams' basket and two more free throws by Roger Mason Jr. sealed a perfect nonconference record for Virginia.
The 11-0 mark, which also includes runaway victories against No. 4 Tennessee and Purdue, is Virginia's first without a loss in non-ACC games since the 1981-82 Cavaliers went 15-0 in Ralph Sampson's junior year.
Missouri, which got 22 points from Clarence Gilbert and 20 from Rush, went nearly 3@1/2 minutes without another point after Rush's fourth 3-pointer gave the Tigers their last lead at 69-68 with 4:19 to play.
With the final minute ticking off the clock, the crowd erupted one more time, chanting "ACC, ACC" while Rush was at the free-throw line.
"When they're that loud, it does great things for a team," Hand said.
And bad things to the opponent, Missouri coach Quin Snyder said.
"We were in the game late, but we didn't make some plays and they did," he said. "We're finding out more and more about ourselves. We're a work in progress and I just want to see our guys continue to invest more in playing the way we need to. Games like this point those things out."
Chris Williams added 17 points and Mason had 13 for the Cavaliers.
Early in the second half, the Tigers seemed primed to take control.
Johnnie Parker capped a 10-3 run to open the half with a one-handed putback dunk that give Missouri a 40-37 lead. Then Mason got hot, scoring his first seven points in a span of just 55 seconds.
After Rush's third 3-pointer brought the Tigers back to even at 45, the lead changed hands several times over the next few minutes.
At one point, Williams' alley-oop dunk gave Virginia 51-48 lead and Gilbert tied it with a 3-pointer 16 seconds later. Just eight seconds later, Hand's 3-pointer restored the Cavaliers' lead, but Gilbert kept the shooting show going, scoring on a driving bank shot to make it 54-53.
Shortly thereafter, Watson made his big move down the middle, the Tigers came up short at the line and the Cavaliers were on their way.
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