The Razorbacks (38-19) must beat Vanderbilt twice on Saturday to advance to the championship game.
Stanek (3-2) limited the Crimson Tide (33-26) to two hits while walking three before leaving after a two-out walk to Taylor Dugas in the eighth. Then Arkansas gave him a bigger cushion with Matt Reynolds' RBI double in the bottom half of the inning.
Trent Daniel retired the final four batters for his third save.
"I thought we played extremely well," Arkansas coach Dave Van Horn said. "It obviously started on the mound. Ryne Stanek threw probably his best game of the year. Good time for it."
Stanek, who was drafted in the third round last year by the Seattle Mariners, had failed to make it out of the first inning last weekend against Mississippi.
"I just had to stay in control," the freshman lefthander said. "The last game out, I lost control. I was rushing everything. You have to have a short memory and work through everything. Otherwise, you're not going to last long.
Robinson went 2 for 3 with a walk and drove in two runs. He led off the fourth with a homer against Alabama starter Jonathan Smart (4-3) and added an RBI single in the sixth.
Robinson sat out the tournament-opening loss to Alabama.
"I was itching to play," the freshman said. "It's my first SEC tournament. I wanted to come out and prove myself and help the team."
Austin Smith drove in Alabama's only run with a single in the fourth after Jared Reaves doubled for the team's only hits. The Tide struggled at the plate for the second straight game after getting shut out by Florida on Thursday.
"Offensively we just had no rhythm," Alabama coach Mitch Gaspard said. "We didn't do a very good job. I thought our energy level was not where I would like to have it. It was kind of low."
And Stanek never gave them much chance to raise it. He struck out five and got the final two batters in the fourth after Van Horn had relievers warming up.
"A couple of experienced hitters came back early in the game and said, 'That guy's really good. He's got really good stuff,'" Gaspard said.