The Raiders (5-6) also snapped a three-game skid to the Titans, winning for just the second time in seven trips to Tennessee.
The Titans (2-9) lost for the ninth time in 10 games after rallying to take a 21-17 lead. They thought they had a game-saving play when safety Michael Griffin broke up a pass in the end zone on fourth down.
But officials flagged B.W. Webb for holding on the other side of the field.
Two plays later, Carr hit Roberts for the winning touchdown. Carr finished with 330 yards and three TDs in his sixth 300-yard passing game this season.
Nate Allen ended the Titans' last chance by intercepting Marcus Mariota with 43 seconds left.
