Roth, the Angels' ninth-round pick in the First-Year Player Draft, improved to 7-0 with a 1.36 ERA in 16 NCAA Tournament appearances. He allowed three runs in 6 1/3 innings in the day's second solid pitching performance by a draftee.
Arkansas right-hander D.J. Baxendale -- the Twins' 10th-round pick -- also tossed 6 1/3 innings, allowing one run on three hits to lead the Razorbacks to an 8-1 win over Kent State earlier in the day.
"I thought D.J. was incredible," Arkansas head coach Dave Van Horn said. "I knew after the first inning he had it, because he threw his fastball right where he wanted it in the first inning and that is a telltale sign for him."
Arkansas (45-20) and South Carolina (46-17) advance to play at 8 p.m. CT on Monday in the winner's bracket, while Florida (47-19) and Kent State (46-19) play an elimination game at 4 p.m.
Both games will be televised on ESPN2 and ESPN3.
Saturday's nightcap was a rematch of last year's championship series, which South Carolina swept, and a marquee pitching matchup between Roth and Florida left-hander Brian Johnson, Boston's first-round pick (31st overall).
The Gamecocks continuously put pressure on Johnson early, but the lefty kept getting out of jams as he stranded seven men on base in the first four innings.
South Carolina finally got the big hit in the fifth. Marzilli (eighth round, D-backs) doubled, first baseman Christian Walker (fourth round, Orioles) singled and right fielder Adam Matthews (29th round, Reds) walked before Erik Payne roped a go-ahead, three-run triple into the right-center field gap.
Johnson was removed, but LB Dantzler and Chase Vergason also had run-scoring knocks to give South Carolina a 5-2 lead.
"We fell behind an awful lot that inning. Like I said, you've got to credit South Carolina's hitters, they did a nice job," Florida head coach Kevin O'Sullivan said. "They got a momentum thing going on right now. And obviously we weren't able to stop it there in the fifth and that was probably the difference in the ballgame."
The comeback erased a misjudged line drive by South Carolina left fielder Tanner English in the third inning that led to two Florida runs. Roth began the inning by allowing consecutive singles, but made the first out on a diving catch on a pop-up bunt.
Florida shortstop Nolan Fontana (second round, Astros) hit a hard grounder up the middle, but Vergason fielded it behind second base and flipped to shortstop Joey Pankake for the force, putting runners on the corners with two outs. Florida right fielder Preston Tucker smoked a liner to left and English initially went in before watching the ball sail over his head.
Marzilli robbed Florida's Daniel Pigott (ninth round, Reds) of an extra-base hit with a diving catch in right-center field to lead off the eighth inning before the Gamecocks added two insurance runs in the ninth.
South Carolina's win was preceded by Baxendale's solid start in the day's first game, as the Razorback right-hander didn't allow a hit until Kent State's Sawyer Polen reached on an infield hit in the fourth inning.
Baxendale lost his shutout in the sixth when Kent State's Jimmy Rider homered, then exited in the seventh with two on and one out before right-hander Brandon Moore record the inning's final two outs.
While Baxendale pounded the strike zone, Golden Flashes left-hander David Starn couldn't find his stuff in the first inning.
A sacrifice bunt by Arkansas' No. 2 hitter was the only time the bat left the shoulders of the first four Razorback hitters as Starn walked the bases loaded. Right fielder Brian Anderson followed with a line drive off Starn's glove to score the game's first run.
Starn escaped further damage with an inning-ending double play, but the tone was set.
"David faced 26 hitters and only two of them swing at the first pitch," Kent State head coach Steve Stricklin said. "They had a plan to be patient, make David throw strikes. David gets a lot of swings and misses on first pitches that are balls. They had a really good scouting report."
Starn settled down to pitch five solid innings -- also allowing a fifth-inning RBI single by Joe Serrano, who had three hits -- before left fielder Derrick Bleeker's two-run double knocked him out of the game in the sixth.
Starn, drafted in the seventh round by the Braves, allowed five runs on six hits and six walks.
Arkansas added three runs in the eighth -- highlighted by a two-run single by Jake Wise, who previously homered -- while Moore allowed only one hit in 2 2/3 innings of relief.
Arkansas 8, Kent State 1
South Carolina 7, Florida 3
Stony Brook vs. Florida St., 5 p.m. ET
UCLA vs. Arizona, 9 p.m. ET