Beavan, 24, allowed just an infield hit and a bloop single while throwing 33 pitches in two frames.
"I'm getting more angle than I've ever been able to get, which I think anybody would tell you is a lot harder to hit," said the 6-foot-7 Texan. "A hitter's swing is side-to-side, so if you get down angle, it's harder for them to square it up.
"That's all I concentrated on, just focusing on my mechanics and not trying to throw harder. All I tried to focus on was staying in my delivery and going to the mitt, and I did that today, so it was fun."
Beavan is competing for one of Seattle's final two rotation slots after going 11-11 with a 4.43 ERA in 26 starts last year.
"He did a nice job," said manager Eric Wedge. "He came out aggressive, was fluid with his delivery and had some pretty good stuff. He's a guy that works pretty hard to keep getting better, and I think that was obvious today.
"He's always done a nice job with his fastball, but his secondary stuff continues to improve. He's being more consistent with his delivery and he's such a big guy, for him to be able to leverage the ball downhill, that's only going to be that much more important for him as he continues to grow."