CHARLOTTESVILLE, Va. --- In the team hotel on the night before his final road game, Clemson running back James Davis decided to make sure his team knew where he stood.

"I said, 'Hey, I'm a senior and this is my last road game. I need this one,' " Davis said he told his teammates. "'I want to go to a bowl game. I want something to be proud of.' "

The Tigers delivered for Davis and 27 other seniors on Saturday, turning three Virginia turnovers into points and playing stout defense in a 13-3 victory that kept alive Clemson's chance of winning its last two regular season games to qualify for a bowl game.

The Tigers (6-5, 4-4 Atlantic Coast Conference) turned two interceptions and a fumble recovery into points, getting enough to win on C.J. Spiller's halfback option touchdown pass in the first quarter.

With two victories against Football Championship Subdivision teams, the Tigers also will need to defeat South Carolina at Death Valley on Saturday to reach the postseason, and the sense of urgency Davis was hoping for fueled their efforts all day.

"That was the only thing we talked about," said defensive back Michael Hamlin, whose interception gave the Tigers the ball at the Cavaliers 20 before Spiller's big pass. The 15-yard scoring pass was the first of Spiller's career.

"I actually thought I overthrew him," he said of Tyler Grisham, who ran what Virginia coach Al Groh said was a common fake and found himself with no defenders anywhere near him.

When Mark Buchholz later added field goals of 32 and 23 yards, the Tigers had more than enough to win. The last was set up by Clemson's third interception of the game.

"This is one that doesn't take a big, thick microscope to dissect," Groh said. "It was pretty obvious."

Despite holding the vaunted tandem of Spiller and Davis to 83 rushing yards, the Cavaliers (5-6, 3-4) lost their third in a row after a four-game winning streak that put them in the race for the ACC's Coastal Division title. Virginia now needs to win next weekend at Virginia Tech to qualify for a bowl, and Groh's teams are 1-6 against the Hokies.

The Tigers led 10-3 at halftime, added a field goal with 2:37 left and a third interception with 1:58 remaining, sending frigid Cavaliers fans streaming to the exits. The temperature at game time, 35 degrees, was the coldest at Virginia in 42 years.