Dalles and Adam Matthews each had four hits for the Gamecocks (40-21), who scored the first 12 runs on the way to an easy victory against the host Pirates (43-18). South Carolina finished with 17 hits, while Cooper (9-4) allowed just two runs and struck out six despite giving up 14 hits.
Dalles hit a two-run homer in the sixth, then hit his slam in the eighth.
Corey Thompson hit a two-run homer for East Carolina, while Seth Maness (9-2) took the loss after allowing six runs and 11 hits in 6 2-3 innings.
Oklahoma State 3, Clemson 2
CLEMSON, S.C. Neil Medchill hit a two-out RBI single in the eighth inning to give Oklahoma State a 3-2 victory over Clemson in an NCAA regional game tonight.
Medchill's sharp grounder went off the glove of sprawling first baseman Ben Paulsen, allowing Micheal Dabbs to score from second with the go-ahead run.
Reliever Randy McCurry (4-1) got the Cowboys (34-22) out of an eighth-inning jam and retired Clemson (41-20) in order in the ninth.
Tom Belza and Mark Ginther broke open a scoreless game with back-to-back homers in the seventh off Tigers starter Casey Harman. Ryan Hinson (2-1) took the loss.
Oklahoma State lefty Andrew Oliver took a shutout into the eighth, but the Tigers tied it on RBI singles by Chris Epps and Mike Freeman.
Utah 11, Georgia Southern 10
FULLERTON, Calif. Michael Beltran's two-out RBI single in the bottom of the ninth inning led Utah to an 11-10 victory over Georgia Southern in an elimination game today.
Rick Cornu was hit by a pitch with one out in the ninth, took second on a passed ball and scored one out later on Beltran's single to left for Utah (27-30), playing in its first NCAA tournament game since 1960.
Corey Shimada, C.J. Cron and Cooper Blanc homered for the Utes. Ty Wright and Griffin Benedict hit home runs for Georgia Southern (42-17), which made its first tournament appearance in seven years.
Greg Krause (3-4) got the win in relief, while Charles Matthews (2-1) took the loss.
Elon 4, Georgia State 3
ATLANTA Cory Harrilchak hit a go-ahead home run, Jimmy Reyes struck out 14 and Elon edged Georgia State 4-3 today to eliminate the Panthers from their first NCAA tournament.
Reyes (8-0) threw 135 pitches and gave up eight hits and three runs in eight innings while setting his career high for strikeouts.
Harrilchak's leadoff homer in the sixth broke a 3-3 tie. Bennett Davis, who hit three homers in a 17-15 loss to Southern Miss on Friday, added a two-run homer in Elon's three-run first inning.
Elon's 138 homers lead the NCAA.