Irving's 15th-inning ground-rule double started the game-winning rally that ended with Daniel Pinero's sacrifice fly, giving the Cavaliers a 3-2 victory moments before the clock struck midnight local time.
"I just went into a two-strike approach kind of, and [TCU's Trey Teakell] threw me another curveball, and I just stayed back and put it in the air and got the job done," said Pinero, who previously missed on two safety squeeze attempts.
Pinero's sac fly -- coming after the Virginia shortstop committed three errors earlier in the game -- keeps Virginia (51-14) undefeated in Omaha, while TCU (48-17) faces Ole Miss (47-20) on Thursday in an elimination game after the Rebels beat Texas Tech, 2-1, with their own walk-off Tuesday afternoon.
"There was kind of a little bit of a lull in the game there from about the ninth until the 15th," Virginia coach Brian O'Connor said. "You've got to string hits together. You've got to find a break in this World Series these days, and it's just they're just tough to win. I'm just really proud of our guys that we found a way."
Thomas Woodruff pinch-ran for Irving -- the D-backs' 34th-round pick in the 2014 First-Year Player Draft -- and advanced to third on a sacrifice bunt before Pinero's fly ball ended the longest game in College World Series history, tied with three other 15-inning affairs, the last of which came in 1970.
"I can't speak for these guys, but they were into it, and they were, like I said, just trying to find a way," O'Connell said. "You look at the pitching on both sides that was being thrown out there, there are some pretty special arms that guys can really pitch."
A breakdown of several of those arms, which turned in filthy pitching performances:
• Virginia left-hander Brandon Waddell held TCU to two runs (one earned) on six hits while fanning five and walking zero over seven innings.
• Virginia righty Nick Howard (No. 19 overall, Reds) allowed one hit and struck out six over four innings, while Whit Mayberry and Artie Lewicki (eighth round, Tigers) each tossed two scoreless innings.
• TCU starter Brandon Finnegan (No. 17 overall, Royals) allowed two runs (one earned) on nine hits over eight innings, striking out five.
• TCU reliever Riley Ferrell tossed four one-hit innings and struck out four, while Teakell tossed 2 2/3 innings of one-run ball in taking the loss.
"The pitching was smothering," TCU coach Jim Schlossnagle said.
Neither team had many scoring opportunities until Pinero's heroics, with TCU getting only two baserunners to second from the fourth inning on and Virginia going hitless in extra innings until Pinero's double.
"Premium arms," Schlossnagle said. "It's hard to get upset at your offense when you're facing that kind of pitching."
The wackiest play came in the bottom of the eighth for Virginia. With Kenny Towns on second with two outs, Derek Fisher (No. 37 overall, Astros) hit a ground ball to shortstop. Keaton Jones' throw pulled first baseman Kevin Cron (14th round, D-backs) off the bag, while Pinero was running hard and ended up caught halfway between third and home.
Cron fired to catcher Kyle Bacak (25th round, Nationals), who threw to third baseman Derek Odell. Odell went back to Finnegan, who was covering home, but the throw was low and snuck by the pitcher. Cron was backing up, snagged the ball and tagged Towns in the face to end the inning.
Other notable defensive plays came in the bottom of the 10th, when TCU center fielder Cody Jones (38th round, Indians) made a diving catch to rob Virginia's Mike Papi (No. 38 overall, Indians) of at least a single, and in the top of the 12th when Virginia center fielder Brandon Downes (seventh round, Royals) threw out TCU's Dylan Fitzgerald at third for the second out of the inning.
The long nightcap followed an Ole Miss walk-off victory, the first time since June 21, 2005 that two walk-offs occurred on the same day of the College World Series.
The Rebels played flawlessly, getting a brilliant pitching performance from left-hander Christian Trent and clutch pinch-hitting from Holt Perdzock and John Gatlin.
Texas Tech, meanwhile, made just two mistakes, but each were pivotal in ending the Red Raiders' season.
Both of Texas Tech's miscues led to Ole Miss runs, including the game-winner, as Gatlin singled home Aaron Greenwood to lift the Rebels to a 2-1 victory.
"We contribute in so many different ways, and when the game is on the line like that, we're each called upon in different situations," Gatlin said. "Every one of us feels like we're prepared for it and expect to get the job done."
Gatlin's knock -- a soft liner over the second baseman -- plated Greenwood, who was pinch-running for Colby Bortles. Bortles drew a one-out walk and advanced to third on a throwing error by Texas Tech pitcher Cameron Smith on a comebacker.
The Red Raiders' other error came in the seventh, when second baseman Bryant Burleson couldn't corral a one-out grounder off the bat of Sikes Orvis. Texas Tech right-hander Ryan Moseley issued a walk, but he got Will Jamison to fly out for the inning's second out before Perdzock hit the first pitch he saw down the third-base line to score Orvis.
Trent (29th round, Dodgers) scattered six hits, walked one and fanned five over eight shutout innings.
Texas Tech finally got on the board in the ninth against right-hander Scott Weathersby, who surrendered a one-out single to Adam Kirsch before pinch-runner Zach Davis stole second and third, and then scored on Anthony Lyons' sacrifice fly.
The Red Raiders also got a strong pitching performance out of Moseley, who allowed four hits, struck out six and walked three in 7 1/3 innings.
"I thought both guys were terrific," Ole Miss coach Mike Bianco said. "I remember looking up at some point and we had three hits and realized we had played like 15 innings [in the College World Series] and only had four hits. Just one of those where you had to get the timely hit."
Ole Miss 2, Texas Tech 1
Virginia 3, TCU 2 (15 innings)
UC Irvine vs. Texas, 8 p.m. ET*
*Denotes elimination game