The top-seeded Volunteers overcame sloppy defensive play and poor pitching, ratcheting up their high-powered offense another notch at the end to win their first CWS opener in five appearances since 2001.
Tennessee (56-12) will play North Carolina in a Bracket 1 winner's game on Sunday night. Florida State (47-16) will meet Virginia in an elimination game in the afternoon.
Moore went 5 for 6 for the Volunteers while becoming the first player to hit for the cycle at the CWS since Minnesota's Jerry Kindall did it against Mississippi in 1956.
Tennessee, which trailed 9-4 in the fifth inning, overcame its biggest deficit to win on the road or at a neutral site since coming from five runs down to win at UC Irvine in 2017.
The Vols, in the CWS for a second straight year and third in the last four, trailed 11-8 entering the bottom of the ninth. Kavares Tears, who homered earlier, tripled leading off and scored on a sacrifice fly.
Moore came to bat with two outs and a runner on base and was down to his last strike against Brennen Oxford (2-1) when he doubled into the left-field corner.
"It was a fight, me against him, mano a mano," Moore said. "I guess I won that."
That brought up Blake Burke, who delivered the tying single up the middle after he might have caught a break when third-base umpire Shawn Rakos signaled Burke checked his swing on a pitch with two strikes.
"It was a check swing and I didn't go," Burke said. "Just kept battling and that was the result."
FSU coach Link Jarrett's body language in the dugout indicated he didn't agree with the check-swing call. He did not directly address the play after the game. Had the call gone the other way, the game would have been over and FSU would have won.
"You guys saw the game," he told reporters. "I need to watch every pitch of this game again. There's factors in this that affect the outcome of the game and I can't tell from 90 feet away on the side what was going on with some of the things that occurred. Every pitch matters in these games and you saw the result of this."
Burke moved to second on Billy Amick's single off Oxford, and then Dreiling drove in the winning run on the second pitch from Connor Hults.
Nate Snead (10-2), the sixth Tennessee pitcher, got the win after holding the Seminoles scoreless on one hit over the last 2 1/3 innings.
Moore, the Vols' leadoff man and a projected top-15 pick in the amateur draft next month, started his big night with a triple, his first since 2022, into the right-center gap in the first inning. He doubled in the second, singled in the fourth and drove the ball 440 feet to straight-away center for his 33rd homer of the season leading off the bottom of the sixth.
"The whole game, I tried to get on base and set the tone," Moore said. "I really, to be honest, didn't know I did it (hit for the cycle)."
The Vols' first walk-off win of the season came after a grinding first half of the game. They committed three errors in a game for only the second time this season. The three errors also matched their most in 21 all-time CWS games. Tennessee pitchers combined to allow 13 hits, walk a season high-tying nine and hit a batter.
The Vols came to Omaha with a school-record 173 homers and averaging 9.2 runs per game for the season and 10.7 for the NCAA Tournament. Burke said it was only a matter of time before the offense cranked up.
"We threw a bunch of jabs the whole game," he said, "and landed the big punch in the ninth."