The Commodores (48-19) are off until Friday as they await the winner of UC Irvine (41-24) and Texas (44-20), which eliminated Louisville, 4-1, in Monday's opener.
The Longhorns and Anteaters play in an elimination game at 8 p.m. ET on Wednesday.
"The game turned around when Walker came in," Vanderbilt coach Tim Corbin said. "There was a momentum change, and he pounded the strike zone from the minute he got in there until the minute the game finished."
Vanderbilt's two-run first inning was quickly overtaken by the Anteaters in the second, as they put four runs on the board against Beede, the 14th overall pick by the Giants in Major League Baseball's First-Year Player Draft.
UC Irvine third baseman Tyler Sparks (second round, Reds) had the biggest hit, a two-run single off Beede, who lasted only 3 2/3 innings while walking three and hitting three batters.
"As I told them when I walked out there, it's the last thing I want to do as a coach, to take him out there, but we needed to change the pace of the game at that point," Corbin said. "You might let a guy like that go a little bit longer, but it was a point in the game where we were losing by two, wanted to keep the game right there."
The Commodores struck back in the fifth inning, getting the first two batters on before shortstop Vince Conde (ninth round, Yankees) had an RBI groundout and Zander Wiel crushed a double to deep left.
Wiel scored the go-ahead run on Norwood's sacrifice fly and Buehler dominated the rest of the way, striking out seven, walking two and hitting one batter.
"We had a good approach against Beede. He tends to be wild, and we were disciplined," UC Irvine right fielder Kris Paulino said. "And Buehler came in the game, he pounded the strikezone. He was throwing pretty hard. He had good command of his offspeed, too. He was on."
The Longhorns remained alive in the loser's bracket thanks to flawless defense behind a stingy pitching performance by right-hander Parker French (19th, Tigers), who allowed just four hits in 7 1/3 innings.
Texas scored one run apiece in the middle three innings, manufacturing its first thanks to left fielder Ben Johnson's sacrifice fly.
The Longhorns took advantage of Louisville's defensive miscues in the next two innings to add on, with the first run coming on an error by shortstop Sutton Whiting on a hard-hit ball up the middle by Texas' Kacy Clemens to score C.J. Hinojosa.
Louisville second baseman Zach Lucas (29th round, Pirates) made two errors in the fifth, the first putting runners on first and second with one out and the other a throwing error allowing Texas' Mark Payton (seventh, Yankees) to score.
That was enough to doom Louisville and right-hander Anthony Kidston, who allowed three runs (two earned) on six hits while fanning five over eight innings to suffer his first loss of the year.
"We had a two-inning lapse there in the middle of the game where we made it a little too easy on them," said Louisville coach Dan McDonnell, whose team finished 50-17. "They got the momentum and we let them roll with it for a couple of innings."
Texas' defense, meanwhile, was superb behind French, highlighted by a couple of nice plays by Hinojosa at short and Brooks Marlow at second. That allowed French to stay focused on Louisville, who was also blanked by lefty Travis Duke over the final 1 2/3 innings.
"I think when I step out there every game, this is probably the best defense in the country. I can say that with confidence," French said. "When they start making those plays, [it] makes me more of a strike-throwing machine because they were going to be aggressive."
Texas 4, Louisville 1
Vanderbilt 6, UC Irvine 4
TCU vs. Virginia, 3 p.m. ET
Texas Tech vs. Ole Miss, 8 p.m. ET