The Arkansas win ties the best-of-three NCAA Super Regional at one game each with a deciding game scheduled for Monday at 6:05 p.m.
The Razorback rally in the ninth began with a leadoff walk to Matt Reynolds against the Baylor closer Max Garner who was in his second inning of work.
Down 4-3 at the time, Dominic Ficociello flied out to short, bringing Brian Anderson to the plate and he hit a scorcher up the middle to put runners on first and second.
Bo Bigham would then hit what could have been a game-ending double play ball to short, but the grounder was booted leaving the bases loaded and extending the inning.
Jimmy Bosco then worked the count to 2-2 before getting hit by a pitch by a pitch bringing in a run in to tie the game.
A Baylor pitching change welcomed John Clay Reeves to the plate and Crayton Bare hit Reeves with the first pitch to allow the winning run to score.
A close game throughout, Arkansas would not have even had a chance to win if it had not been for some outstanding pitching in the late innings.
The Arkansas bullpen allowed two runs on four hits over five innings, but got out of several jams including a bases loaded, no out fiasco in the eighth.
Josh Ludy was hit by a pitch to lead off the inning and Max Muncy drew a four-pitch walk to put runners on first and second.
A bunt single up the third base line by Dan Evatt loaded the bases with nobody out. Barrett Astin then got Cal Towey to strike out swinging for the first out and then induced a 6-4-3 double play from Lawton Langford to end the inning and keep the score at 4-3.
The play was started by Tim Carver who ranged to his right and threw a strike to Bigham across his body who completed the double play with a strong throw to first.
Arkansas struck first, scoring once in the bottom of the first. With one out, Joe Serrano lined a triple to the left-center field alley.
Reynolds then hit a sacrifice fly to right to drive in Serrano.
Baylor tied the game with a run in the top of the third. Nathan Orf struck out to begin the inning, but was able to reach first on a wild pitch.
Logan Vick then walked to put runners on first and second.
Another wild pitch advanced Orf to third with nobody out. Ludy hit a fly ball to shallow center that was caught by Matt Vinson.
Orf attempted to tag from third on the fly out, but Vinson threw a strike to home to throw out Orf for the double play.
A stolen base advanced Vick to second and he came around to score the tying run on a single to center field by Muncy.
The Razorbacks regained the lead with a pair of runs in the bottom of the third. After the first two batters of the inning were retired, Serrano and Reynolds hit back-to-back singles to put runners on first and third.
Dominic Ficociello then laced an opposite field double down the right field line, scoring both runners to give Arkansas a 3-1 lead.
The Bears took their first lead of the game with three runs in the top of the fifth.
After a leadoff walk by Adam Toth to begin the inning, Orf reached on an infield single to put runners on first and second.
Vick then singled to center field, scoring Toth and advancing Orf to third. Vick stole second to put runners on second and third with nobody out.
Back-to-back groundouts by Ludy and Muncy scored Orf and Vick to give the Bears a 4-3 lead.
Monday's game time has been set for 6:05 p.m. and will be televised on ESPN2.