The victory gives Arizona (47-17) a 1-0 lead in the best-of-three series against South Carolina (49-19). Game 2 is at 7 p.m. CT on Monday.
"[Wade] was just spot on," Mejia said. "He just keeps [going] and it's easy to play defense behind him."
Right fielder Robert Refsnyder -- the Yankees' fifth-round pick in the 2012 First-Year Player Draft -- went 2-for-3 with a two-run home run in the first inning to back Wade, while Mejia (fourth round, Cardinals) later drove in a run.
Wade, a sophomore, allowed one run on six hits and walked only one in his second complete game of the College World Series after also throwing all nine against UCLA. He is the first pitcher to throw consecutive complete games in Omaha since Jason Windsor (Cal State Fullerton) in 2004. Wade, who also went the distance in the Super Regionals, is the first player since 2005 to throw three consecutive complete games in the NCAA Tournament.
"I knew that they were a pretty aggressive team and they were going to try to take the extra base," Wade said. "I tried to work ahead and get in counts that were favorable to me."
Wade's effort puts Arizona one win away from its first NCAA championship since 1986. The Wildcats are 9-0 in the NCAA Tournament and are looking to become the 14th different team to win a title without losing a tournament game.
"You have to come out tomorrow and play good baseball," head coach Andy Lopez said. "We understand where we're at. These guys understand who they're playing. They understand it's not a tournament somewhere in South Dakota. ... So they've got to play good baseball again."
The two-time reigning champion Gamecocks are one loss away from seeing their quest for a three-peat end in disappointment. The team that wins Game 1 in the championship series has won the title seven out of nine times, but South Carolina is used to staving off elimination after advancing to the finals through the loser's bracket.
"It's a best-of-three-game series for a reason. We have to come out and fight tomorrow," South Carolina catcher Grayson Greiner said. "We were in the same situation a few days ago. They've got to beat us twice to win the championship, and the best team will have to win two games."
Mejia's play in the first inning came after South Carolina's Joey Pankake reached on a grounder through the legs of third baseman Seth Mejias-Brean (eighth round, Reds). Evan Marzilli (eighth round, D-backs) hit a grounder up the middle, but Mejia made a diving stop behind the bag to start a 6-4-3 double play.
Refsnyder homered to the opposite field in the bottom of the inning for an early 2-0 lead.
"I knew if we got the team on the board right there ... [it would] kind of settle the team down so we could just go out and play good baseball," Refsnyder said. "I was fortunate enough to run into it."
The homer was enough cushion for Wade, who allowed only one hit until the sixth. After Greiner led off with a double, Wade induced two fly balls before Marzilli's two-out single plated the Gamecocks' only run.
It was the only inning South Carolina put more than one runner on the bases, as Refsynder nabbed right fielder Adam Matthews (29th round, Reds) when Matthews tried to advance to third on Kyle Martin's single in the seventh.
"He had a lot of good sink on his fastball and we got runners out there, but he made a big pitch when he needed to make a big pitch and you have to give him credit for that," Greiner said. "He pitched a great game and got them the win."
While Wade held the Gamecocks in check, the Wildcats continued to tack on runs. Mejia and Mejias-Brean had RBI singles in the third and fifth while Refsnyder drove in his third run of the game with a single in the seventh against right-hander Evan Beal.
Beal was removed in the eighth with two on before South Carolina right-hander Tyler Webb got Refsnyder swinging with the bases loaded to end the inning.
"They can swing it, as you can see. But I don't think it's anything really insurmountable to go out there and at least force the Game 3," Beal said. "It's going to be tough, but we have to get back on our game tomorrow and we have to get some runs."
College World Series finals results and schedule
Sunday: Arizona 5, No. 8 South Carolina 1
Monday: Arizona vs. No. 8 South Carolina, 7 p.m.
Tuesday: No. 8 South Carolina vs. Arizona, 7 p.m. (if necessary)