Vanderbilt (54-11) beat the Tar Heels for the second time in the CWS and plays Southeastern Conference rival Florida on Friday. The Commodores are in Omaha for the first time and would need to beat the Gators twice to reach next week's best-of-three finals.
The Commodores have to face a Florida team that has beaten them in four of five meetings this season, including 3-1 at the CWS.
North Carolina (51-16) left 34 runners on base in its three CWS games and was just 7 for 39 with runners in scoring position.
Hill (6-1) outdueled Greg Holt (7-2) in a matchup of Washington Nationals draft picks.
Hill, taken in the sixth round, allowed a run and four hits in seven innings.
Holt, an eighth-rounder who was making his second start of the season, lasted 2 2-3 innings. He gave up five runs and four hits, leaving after Casali's homer made it 5-0.
The Tar Heels couldn't advance a runner past first base after they scored in the fifth.
Hill worked out of trouble that inning after Ben Bunting's RBI groundout left first base open. Hill intentionally walked All-America Colin Moran with two outs to face Jacob Stallings, who had doubled in his first two at-bats. Stallings fouled off an 0-2 pitch barely outside the left-field line, then swung and missed at strike three.
Williams, who has pitched 5 2-3 scoreless innings in three CWS appearances, came on to start the eighth.
Harrell's three-run homer put Vanderbilt up 4-0 in the second inning. It was his second in three games here and ninth of the season.
The Commodores opened the scoring when Tony Kemp led off the game with a triple into the right-center gap and scored on a sacrifice fly.