Will Allen drove in the go-ahead run in the seventh inning,
Ole Miss (48-20) will play
It was the most runs allowed by TCU (48-18) in 16 games.
Allen, who was 0 for 8 in the CWS when he came to bat in the third inning, went three for five with three RBIs.
Josh Laxer (3-2) worked 22/3 innings of relief for the win, and Aaron Greenwood went the last 11/3 innings for his fifth save. Jordan Kipper (8-3), who relieved struggling TCU starter Tyler Alexander, took the loss.
Allen had a two-out, two-run double in the second for a 3-0 lead, the tiebreaking base hit in the seventh, and he scored an insurance run after he singled in the ninth.
Alexander, TCU's first 10-game winner in four years, struggled for a second straight start after winning 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 at 3-3. That marked the first time an inherited runner scored against the Rebels' bullpen in nine
Each team added a run in the fifth, with Cron driving Laxer's high fastball 10 rows into the left-field stands for the CWS' second homer in 10 games.
Laxer and freshman Wyatt Short combined to retire nine straight after that. 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.