Allen, who was in the lineup as the designated hitter on Thursday night to rest a sore shoulder, snapped out of a mini-slump with three hits and three RBIs to lead Mississippi past TCU 6-4 at the College World Series.
Ole Miss (48-20) advanced to play No. 3 national seed Virginia on Friday night. The Rebels would need to beat the Cavaliers (51-14) on Friday and again Saturday to reach next week's best-of-three championship series.
The other bracket has unbeaten Vanderbilt (51-14) against Texas (45-20).
Allen and Sikes Orvis combined for six of the Rebels' 11 hits on a warm, calm evening that provided more favorable conditions for offense at TD Ameritrade Park.
"Winds not blowing in 20 mph, it's a little different here," Ole Miss coach Mike Bianco said. "We were able to barrel some balls up and get some hits."
The Rebels put up the most runs allowed by TCU (48-18) in 16 games, and they did it against a pitching staff that came in with a nation-leading 2.16 ERA.
Ole Miss won its fourth elimination game in the NCAA tournament.
"It's just something with this team, when our back's up against the wall, we play really good baseball," Allen said. "Just a tough team, a very confident team. And we've continued to do it throughout the whole season."
Allen, a .336 hitter for the year, was batting .219 in his previous eight games and was 0 for 8 in the CWS when he stepped to the plate in the third inning. His two-out, two-run double produced a 3-0 lead, he had the tie-breaking base hit in the seventh, and he scored an insurance run after he singled in the ninth.
Yes, taking the night off from catching helped. Allen had been struggling with a sore right shoulder the entire postseason. Austin Knight played a strong game behind the plate and set up a run in the third inning with a sacrifice.
Allen said the DH's role didn't change his approach.
"You just have to stay in the game and cheer on your teammates," he said. "There is a tunnel back there where I can go and loosen up and take some swings as I see my at-bat coming closer."
Three Mississippi relievers held TCU without a hit after Kevin Cron's homer in the fifth. Josh Laxer (3-2) worked 2 2-3 innings of relief for the win, and Aaron Greenwood went the last 1 1-3 innings for his fifth save.
Jordan Kipper (8-3), who relieved struggling TCU starter Tyler Alexander, took the loss.
Alexander, TCU's first 10-game winner in four years, struggled for a second straight start after he won six in a row. He gave up consecutive hits to start the fourth and left with his team down three runs.
Ole Miss starter Sam Smith lost his control and didn't make it out of the fourth, either. Laxer came on with the bases loaded and issued a two-out walk to Cody Jones that tied it 3-all. Derek Odell hit a long fly that J.B. Woodman caught near the warning track to end the inning.
Each team added a run in the fifth, with Cron driving Laxer's high fastball 10 rows into the stands in left field for the CWS' second homer in 10 games.
"It doesn't quite feel the same now that we didn't get the win, but at the time, it was a big part of the game to get that run back," Cron said. "But it's somewhat bittersweet, obviously."
Laxer and freshman Wyatt Short combined to retire nine straight after Cron's homer. TCU threatened in the eighth, putting runners on first and second with one out. But Short struck out Dylan Fitzgerald, and Greenwood came on and got Keaton Jones to ground to shortstop, with Errol Robinson pumping his fist after throwing out Jones.
"We set the table a couple times, and it just wasn't meant to be," TCU coach Jim Schlossnagle said.