The loss drops the Hoosiers (49-15) to the losers bracket, where they'll face Oregon State (51-12) at 8 p.m. ET on Wednesday. The Beavers opened action Monday by defeating Louisville, 11-4, in an elimination game.
The Bulldogs (50-18) await the winner of that game for a 3 p.m. matchup on Friday and are one victory away from advancing to the College World Series final.
They're in that position largely because of of Girodo, who entered in the third inning on Monday and didn't exit until there was one out remaining. In between, the Blue Jays' ninth-round pick in the 2013 First-Year Player Draft constantly pitched out of trouble -- allowing seven hits -- but was dominant when he needed to be.
"Chad just battling and battling and battling," Mississippi State coach John Cohen said. "I thought when he had second and third with one out there in the fifth and they didn't score, I thought that was the story of the ballgame."
While Girodo turned in the gutty pitching performance, Trey Porter delivered the big hit.
Mississippi State' designated hitter hit a go-ahead single in the eighth inning to score two -- including left fielder Demarcus Henderson, who had tied the game with an RBI single.
Porter was in a similar situation two innings earlier -- pinch-hitting with the bases loaded and the Bulldogs down two -- but his drive to right-center field wasn't deep enough to leave the yard.
"I just happened to step in the box when the game was on the line and anybody else could have stepped up on this team, that's how we are," Porter said.
The Hoosiers got solid pitching performances out of freshman lefty Will Coursen-Carr and right-handed reliever Ryan Halstead (Twins' 26th-round pick) before the Bulldogs broke through in the eighth. Until scoring once and leaving the tying run on third in the ninth inning, the Hoosiers were unable to get much going after of the early innings. Indiana managed only five hits after the third and stranded 10 baserunners.
"We had plenty of guys on base in scoring position and we just didn't move the ball," Indiana coach Tracy Smith said.
Errors and sloppy play ended Louisville's time in Omaha in Monday's opening game, as Oregon State took advantage of four Cardinals errors in an 11-4 win to stay alive in the losers bracket.
After scoring three in the third inning, Oregon State broke open the game in the fourth, scoring seven runs -- all of which came with two outs.
Center fielder Max Gordon knocked a one-out hit before the Beavers recorded three consecutive two-out singles to chase Cardinals right-hander Jeff Thompson. Reliever Cody Ege fared no better, facing three batters -- walking one and hitting another, while the other reached on Louisville's final error of the day.
Gordon capped the inning with a two-run single, his second hit of the inning.
Thompson, the Tigers' third-round pick, was charged with seven runs (three earned) in 3 2/3 innings. Beavers left-hander Ben Wetzler earned the victory, allowing three runs and striking out six in 6 1/3 innings.
Second baseman Andy Peterson led the Oregon State offense by going 3-for-4 with three runs scored, while Tyler Smith (Seattle's eighth-round pick), Michael Conforto and Gordon had two hits apiece.
"We got into some pitch counts and we knew Ben would give us a good start," Oregon State coach Pat Casey said. "I think it's always good [to get that first win]. Takes a little edge off the players if they can get a win in Omaha."
Louisville (51-14) saw its season end while committing 13 errors in seven postseason games.
"I'm sure our guys are very disappointed, just didn't play well, didn't play clean there in the third and fourth innings and it got out of hand," Louisville coach Dan McDonnell said. "Unfortunately that happens, especially when you're playing a really good opponent."
Mississippi State 5, Indiana 4
Oregon State 11, Louisville 4
North Carolina vs. Louisiana State, 3 p.m.*
North Carolina State vs. UCLA, 8 p.m.
*Denotes elimination game.