Bauer began the inning by allowing a single to Jurickson Profar, walking Tommy Pham, and throwing a wild pitch. He eventually worked out of the jam by getting Austin Nola to pop up and striking out Victor Caratini and Ha-seong Kim.
The pitcher could be seen pointing to his eye as he walked off the mound after striking out Kim.
Bauer said it wasn't the first time he's pitched with one eye closed, adding that he does it to challenge himself.
"I like making myself uncomfortable and throwing different stuff my way and trying to find a solution for it," Bauer said, according to Mike DiGiovanna of the Los Angeles Times. "That's how you improve. Find a way to make yourself uncomfortable, then get comfortable with it and do it again."
He added: "I figured if they can't score off of me with one eye open, it will be difficult to score off me with two eyes open. Just having a little bit of fun. There's definitely a reason behind it ... if I wanted to share, I would have already."
The 30-year-old pitched three innings against the Padres, allowing two hits and striking out three while throwing 36 of his 52 pitches for strikes.